Have any Catholics (e.g. Eastern Rite) ever followed the Old Calendar since the late 16th century? This question occurred to me after reading this question about the observance of Lent among Eastern Rite converts.



It is my understanding that since 1582, the Roman Catholic Church has followed the Gregorian calendar.

The calendar having been a product of the post-Schism Roman Church, Eastern Orthodox were loathe to accept it - some for 5 centuries.  Some majority Eastern Orthodox countries (e.g. Greece) were still subscribing to the Julian Calendar that had been in place during New Testament times as late as 1923.  



While all Eastern Orthodox countries (as far as I know) today observe the Gregorian calendar for civil purposes, some Orthodox jurisdictions (e.g. Russia) still observe the Julian calendar for religious purposes.  Within the Eastern Orthodox Church we have the somewhat bizarre situation of virtually all (if not all) jurisdictions observing the Julian calendar with respect to the Triodion and the Pentecostarion - the periods leading up to and including Easter ("Pascha") and Pentecost, respectively - but some holding to the Gregorian calendar otherwise.  



Given the affinity between Byzantine Rite Catholics and the Eastern Orthodox Church, I was wondering if there are any Byzantine Rite Catholics or other Rites that at any time during the year observer the old Julian calendar for some purpose; perhaps along the line of New Calendar Orthodox jurisdictions more or less holding to the Old Calendar during the Paschal season.
Have any Catholics (e.g. Eastern Rite) ever followed the Old Calendar since the late 16th century?

Since 1923 Eastern Rite Catholic follow a modified Gregorian calendar, while keeping some of the nuances of the Julian calendar.


  Traditionally, the Eastern Orthodox and Byzantine Catholic churches use the Julian Calendar to calculate their feast days. Beginning in 1924 the Patriarchate of Constantinople made an adjustment to their liturgical year to bring the fixed cycle in conformity to the modern Gregorian Calendar. The Paschal cycle, however, continued to be calculated according to the Julian Calendar. This composite calendar is known as the Revised Julian Calendar. Constantinople's example was followed by the Church of Greece as well as a number of other autocephalous churches. Today, some churches continue to follow the Julian Calendar while others follow the Revised Julian Calendar.
  
  In 1923 the Eastern Rite Churches adopted a modified form of the Gregorian Calendar. October 1, 1923, in the Julian Calendar became October 14, 1923, in the Eastern calendar. From this we see the celebration of Christmas on January 7th and New Year's on January 14th. 
  
  The date of Easter is determined by reference to modern lunar astronomy (in contrast to the more approximate lunar model of the Gregorian system). If you wish to see how these dates are calculated, the Astronomical Society of South Australia has an excellent page showing how it's done. - Український Католицький Собор Успення Пресвятої Богородиці


Wikipedia explains it this way:


  Traditionally, the Eastern Orthodox and Byzantine Catholic churches used the Julian Calendar to calculate their feast days. Beginning in 1924 the Patriarchate of Constantinople made an adjustment to their liturgical year to bring the fixed cycle in conformity to the modern Gregorian Calendar. The Paschal cycle, however, continued to be calculated according to the Julian Calendar. This composite calendar is known as the Revised Julian Calendar. Constantinople's example was followed by the Church of Greece as well as a number of other autocephalous churches. Today, some churches continue to follow the Julian Calendar while others follow the Revised Julian Calendar. Only the Orthodox Church of Finland has adopted the Western calculation of the date of Pascha (see computus); all other Orthodox Churches, and a number of Eastern Catholic Churches, celebrate Pascha at the same time, according to the ancient rules. - Byzantine Rite


A Ukrainian Website site puts it this way:


  Outside of the U.S. and Western Canada, many Ukrainian Catholics, especially those in Ukraine, follow the Julian ("Old") Calendar as opposed to the Gregorian ("New") Calendar. The latter is used by the Western Churches — Catholic and Protestant — and in all civil societies. In these ways and others, Ukrainian Catholics may seem more Eastern Orthodox than Roman Catholic. - What is Ukrainian Catholic?