Was Eastern-Orthodox liturgical music influenced by Islam? If you ever went to an Eastern-Orthodox service, well... their music sounds like Islam to me. It's very different from Western Christian music that is typically accompanied by an organ (even known that instrument was developed in the old Byzantine Empire, it was never used in byzantine liturgy because they forbid it, for some reason...)
Was Eastern-Orthodox liturgical music influenced by Islam?

The short answer is: It is seriously doubtful.

It is seriously doubtful considering that the Prophet Mohammad (c. 570 AD – 8 June 632 AD) only came on to the world scene in the late 6th to early 7th centuries. It may in fact be that the opposite could be true. 


  The Pre-Byzantium Era
  
  In the centuries before Constantine, there are no musical manuscripts-all the musical evidence is late; we have no music which is datable with the appearance of the liturgical hymn texts. But if our later musical sources have preserved for us even the essential features of the melodies with which these liturgical texts were first associated, they will enable us to form an idea, however partial, of what the earliest stratum of Christian music must have been like. The insoluble problem of Early Christian music is: how can one make deductions from the evidence in our earliest surviving musical manuscripts? To what degree does the music they contain reflect that of an earlier period? "Throughout the early Christian world," writes Oliver Strunk, "in impenetrable barrier of oral tradition lies between all but the latest melodies and the earliest attempts to reduce them to writing." While it may be possible to date an early musical manuscript, it is virtually impossible to say how old the melodies in it are. The entire question may be seen not so much in terms of a faithful melodic preservation but rather as the degree to which traces of an ancient model may be gleaned from our earliest notated sources.
  
  A marked feature of liturgical ceremony was the active part taken by the people in its performance, particularly in the saying aloud or chanting of hymns, responses, and psalms. The terms chorós, koinonía, and ecclesía were used synonymously in the early Church. In Psalms 149 and 150, the Septuagint translated the Hebrew word machol (dance or festival group) with the word chorós. As a result, the early Church borrowed this word from classical antiquity as a designation for the worshipping, singing congregation both in heaven and on earth. Before long, however, a clericalizing tendency soon began to manifest itself in linguistic usage, particularly after the Synod of Laodicea, whose fifteenth Canon permitted only the canonical psáltai to sing at the services. The word chorós came to refer to the special priestly function in the liturgy-just as, architecturally speaking, the choir became a reserved area near the sanctuary-and the chorós eventually became the equivalent of the word kléros.
  
  For the earliest period, however, authorities are fairly well agreed that the background of the worship service is to be found in Jewish ceremonies of that day, and a large degree of continuity between the worship of the Jewish and Christian communities cannot be doubted. What holds for primitive Christian worship in general is no less true for the earliest Christian music in particular. A strong case can be made to support the belief that the background for the earliest Christian music is to be sought in the music of the Hellenistic Orient, and more specifically in the musical theory and practice of Hellenized Judaism of that day. The Old Testament had a conspicuous place in the thought and worship of the New Testament Church. Old Testament quotations and allusions, especially from the Book of Psalms, abound in the literature of the New Testament, and a comparison of the oldest Jewish liturgical poems with those of Eastern Christians points to a relationship between Syriac and Hebrew poetry, thus establishing the possibility of Jewish influence upon Christian liturgical poetry. We know that cantors of Jewish origin were often appointed, even attracted to teach Christian communities the cantillation of scriptural lessons and psalmody. In this, the ancient manner of oral tradition did not fail to show its inescapable vigour.
  
  The Origins of Byzantine Music
  
  Byzantine liturgical music did not come about in a cultural vacuum. It has its origins in the desert and in the city: in the primitive psalmody of the early Egyptian and Palestinian desert communities that arose in the 4th to 6th centuries, and in urban centres with their cathedral liturgies full of music and ceremonial. It is this mixed musical tradition that we have inherited today-a mixture of the desert and the city. In both traditions-that of the desert and that of the city-the Old Testament Book of Psalms (the Psalter) first regulated the musical flow of the services. It was the manner in which this book was used that identified whether a service followed the monastic or the secular urban pattern.
  
  In the desert monasteries psalms were sung by a soloist who intoned the verses slowly and in a loud voice. The monks were seated on the ground or on small stools because they were weakened by fasts and other austerities. They listened and meditated in their hearts on the words which they heard. The monks gave little thought to precisely which psalms were being used-they were little concerned, for example, with choosing texts that made specific reference to the time of the day; that is, psalms appropriate to the morning or ones appropriate to the evening. Since the primary purpose of the monastic services was meditation, the psalms were sung in a meditative way and in numerical order. The desert monastic office as a whole was marked by its lack of ceremony. 
  
  But in the secular cathedrals the psalms were not rendered in numerical order; rather, they consisted of appropriate psalms that were selected for their specific reference to the hour of the day or for their subject matter which suited the spirit of the occasion for the service. The urban services also included meaningful ceremonies such as the lighting of the lamps and the offering of incense. Moreover, a great deal of emphasis was placed on active congregational participation. The psalms were not sung by a soloist totally alone but in a responsorial or antiphonal manner in which congregational groups sang a refrain after the psalm verses. The idea was to have everyone involved in an effort of common celebration: there was no place here for individual contemplation.u
  
  Thus, it is not until the fourth century, when Christianity and paganism collide as a result of Constantine's mass conversions, and when imperial ceremony entered liturgical solemnity in new and vast cathedrals, that music rears its formidable voice. And even then it did so under very special circumstances, and not without considerable monastic opposition. The monks of the desert likened tunes to demonic theatre, to false praise and to idle pleasure, satisfying the weak-minded and those of little faith and determination. But this does not mean that the monks did not chant. Their rejection was of worldly music, musical exhibitionism and the singing of non-scriptural refrains and chants. It was, in fact, the monastic population that later produced the first and finest hymnographers and musicians-Romanos the Melodist, John Damascene, Andrew of Crete, and Theodore the Studite. And it was the monastic population that also produced the inventors of a sophisticated musical notation which enabled scribes to preserve, in hand-written codices, the elegant musical practices of the medieval East. - [A Brief Survey of the History of Byzantine and Post-Byzantine Chant](https://www.stanthonysmonastery.org/music/History.pdf by Dimitri E. Conomos Oxford University)


What is more interesting is the fact that St. Ephrem (306 - 373) wrote wrote many religious hymns well be before the advent of Islam.


  St. Ephrem [ܡܪܝ ܐܦܪܝܡ ܣܘܪܝܝܐ, literally “fruitful”] was a 4th-century Deacon, Hymnographer, Poet, and Theologian whose beautiful encomiums to the Blessed Virgin Mary continue to draw the admiration of catholic Christians all over the world. He is venerated by the Coptic Orthodox, Syriac Christians, Nestorian Church of the East, Chalcedonian Orthodox, the Roman Catholic Church, and even attracts the veneration of the Anglican Communion. Pope Benedict XV (1914-22) elevated St. Ephrem to the dignify of being a Doctor of the Universal Church. The Pope made a remarkable description of this beloved Saint: “This Harp of the Holy Spirit [Ephrem] never sings weeter songs than when he has set his strings to sing the praises of Mary” (Acta Apostolicae Sedis, 1920, Pg. 467) .  Although many are lost, it is counted that he wrote over 400 hymns. The 5th-century Greek Historian Sozomen, in his famous “Ecclesiastical History” (Book III) speaks very eloquently of St. Ephrem, and his brief description of this awesome Saint is worth sharing, though a bit lengthy. - Holy Ephrem the Syrian on The Blessed Virgin Mary, 306-373 AD


Gregorian Chant as well as Byzantine Chant may have some of the same melodies sang by the Jewish communities of the Early Church.


  The notation of Jewish cantillation and the "neumes" or signs of early Gregorian chant before the adoption of staff notation are similar to the Jewish ones as they emerged as visual "graphs" from hand gestures that give those who live within the oral musical tradition an understanding of varied musical phrases, as opposed to individual notes. This system is still in use in Jewish synagogues around the world. Finally, Werner provides the readers charts of almost identical pieces of Gregorian chant with synagogue melodies.
  
  Curiously, once Christianity had distanced itself from its Hebraic origins in the fourth and fifth centuries, there emerged written accounts of senior Christian authorities like St. Augustine warning of deviation from the old tradition of singing in the Church -- implying an adherence to the musical traditions that came from Jerusalem. Despite the regional evolution of different kinds of church music, some early church fathers declared later musical innovations to be heresy. -  What Did Jesus Sing?


So it is clear that both Byzantine Chant and Gregorian Chant were not influenced by Islamic Chant. Whether or not Islamic Chant was influenced by Byzantine Chant or Jewish Chant is beyond the scope of this question, but I suspect the later may be true in this historical circumstance.