St. Augustine's views on salvation through coercion This question goes out to any denomination.

Why was St. Augustine okay with using force to convert unbelievers to the faith, which also resulted in the eventual Roman Catholic Church's inspiration for the Crusades?

As mentioned by Bruce Shelley in his book "Church History in Plain Language":


  For Urban and the popes who followed him the Crusades were a new type
  of war, a Holy War. Augustine had laid down the principles of a “just
  war”: It was conducted by the state; its purpose was the vindication
  of justice, meaning the defense of life and property; and its code
  called for respect for noncombatants, hostages, and prisoners. All
  these evaporated in the heat of the holy cause. Urban appealed for
  crusaders in the name of the church; the purpose of the Crusades was
  the conquest of the infidels in the Holy Land; and this high calling
  excused somehow the total disregard for noncombatants and prisoners.


Also per this link:


  Urban pulled ideas from St. Augustine to justify the calling of a holy
  war to get rid of enemies of Christianity, and Urban had Pope Gregory
  VII to thank for already having a group loyal to the papacy so Urban’s
  work on power was already partially done (Asbridge, 25-28). Asbridge
  points out that “A central feature of Urban’s doctrine was the
  denigration and dehumanisation of Islam (33).”


As a follow up what caused him to be for that strategy when it came to conversion?
This is a highly controversial topic as there are many people that have a high view of Augustine. However, what He introduced in to the Church is nothing less than Gnosticism. The more I read the ante-Nicean (prior to the council) church writings, the more I see our view of scripture is not nearly as literal as there's was. 

Augustine spent years as a disciple of Manichean Gnosticism. This group denied man's free will, man's ability to cease sinning, and that God has pre-determined some for hell and some for Heaven. When Pelagius debated Augustine, Pelagius largely quoted what Augustine believed before he became a disciple of Mani.

Here are a couple of quotes from Church leaders before Augustine;


  I find, then, that man was constituted free by God. He was master of
  his own will and power…For a law would not be imposed upon one who did
  not have it in his power to render that obedience which is due to law.
  Nor again, would the penalty of death be threatened against sin, if a
  contempt of the law were impossible to man in the liberty of his
  will…Man is free, with a will either for obedience of resistance. (c.
  207, Vol. 3, pp. 300-301) (Tertullian)
  
  And again, who are they that have been saved, and received the
  inheritance? Those doubtless who do believe in God and who have
  continued in His love… and innocent children, who have had no sense of
  evil. (Irenaeus)
  
  There is set before us life upon our observance [of God’s precepts],
  but death as the result of disobedience, and every one, according to
  the choice he makes, shall go to his own place, let us flee from
  death, and make choice of life. (Ignatius)
  
  We…have believed and are saved by voluntary choice (c. 195, Vol. 2, p.
  217) (Clement of Alexandria)
  
  Thus although we are born neither good nor bad, we become on or the
  other and having formed habits, we are with difficulty drawn from
  them. Pg 273 vol.8 (Clement)
  
  Certain ones of those [Gnostic’s] who hold different opinions misuse
  these passages. They essentially destroy free will by introducing
  ruined natures incapable of salvation and by introducing others as
  being saved in such a way that they cannot be lost. (Origen)


This is a common theme in their writings - and all of these opinions of were formed through a plain literal reading of what scripture plainly says. 


  Only this have I found: I have discovered that God made men upright,
  but they have sought out many schemes. - Ecclesiastes 7:29
  
  And the little ones, whom you said would become captives— your
  children who do not know good from evil, will enter the land I give
  them and possess it. - Deuteronomy 1:39
  
  But if it is unpleasing in your sight to serve the LORD, choose for
  yourselves this day whom you will serve - Joshua 24:15a
  
  “Why are you angry,” said the LORD to Cain, “and why is your face
  downcast? If you do what is right, will you not be accepted? But if
  you refuse to do what is right, sin is crouching at your door; you are
  its object of desire, but you must master it.” - Genesis 4:6-7


The use of force was precipitated because He denied mankind's God given free will. He denied our ability to choose, and put upon mankind a "ruined nature" that had to be baptized out with a sprinkling as a baby.

As some additional resources I highly recommend checking out the scroll publishing channel on YouTube, that has the majority of their audio CD's. I also recommend using the Early Christian Dictionary and comparing it to scripture and what is taught today. 

Let God be true, and every man be a liar.