In a short answer to the title of this post, one word is sufficient. Yes. This topic divides, even more than any other Christian doctrine it seems. Tempers can flare and world-views are challenged whenever this doctrine comes up. For some, the word predestination is a high and lofty theological word. Tradition gets in the way of interpreting the scriptures, so much so that even devoted Christians don't even know that the word predestine (Romans 8:29, Ephesians 1:5, Acts 4:28) is even in the bible. This is because people fail to identify their presuppositions when reading the Bible; so, when words like election and predestination come up, the tradition broom comes and sweeps them away. Yes, this subject divides, but does that mean that conversation stops?
Whenever this issue comes up, someone is bound to say "hey what you are doing is divisive and Jesus doesn't like it!" Notice that this is essentially a conversation stopper. No arguments are actually addressed. Discussion stops because what the synergist does is more or less throw out a red herring. When the synergist's arguments fail, they reach into their back pocket next to Servetus and pull out the ole "dividing the body" card. It should be obvious that whenever two parties disagree, there is division, one on one side and the other on the other side. That is the nature of disagreements. Division. So when that card is pulled, its like saying "stop disagreement", "move along and stop talking about this."
Now don't get me wrong, I want to be united with my brothers and sisters in Christ, but that unity is to be in TRUTH. There is a tendency in modern evangelicalism, which has been brought in by secularism, to promote love over truth. Why? Because love is easier and it's a nice, warm and fuzzy concept that everyone can agree on. I often hear "I guess in the end it doesn't really matter." This is another tactic for avoiding conversation. What it does is protect the person from being wrong, and it just puts the subject in the back of the mind. This one is especially mind boggling to me because on any other doctrine, whether it be the trinity or the deity of Christ, Christians seek to be correct. What you believe about God will change your life. Would any true Christian say "well I guess the doctrine of hell doesn't matter" simply in virtue of its divisive nature?
One other conversation stopper I frequently hear is "they are both wrong". You certainly won't hear a Calvinist making that argument. I really think this one is simply disingenuous or just mistaken, because asking about what this person believes will most of the time unveil some type of synergistic system. It also fails to take into account that Calvinism and Arminianism, monergism and synergism, are two completely different systems of thought, and that there simply is not a middle ground. Four point Calvinists are not Calvinists. You cannot hold to unconditional election and then turn around and deny limited atonement--well I guess you could if consistency isn't a matter you hold in high regard. As if the atonement could be for the elect and non-elect, in which case the words atonement, and elect would lose all meaning. This is why historically the doctrine of substitutionary atonement has been a reformed doctrine. You can't be crucified with Christ and at some point not be crucified with Him, and not gain the benefits of the atonement(Galatians 2:20, Romans 8:29-34). If someone has their sins atoned for then that means they will be justified. Early Arminians recognized this and by doing so they adopted what is called the governmental theory of the atonement, which says that Christ suffered because of sin and didn't die for it.
"You worship Calvin and not Jesus." Absurd as this comment is, amazingly it still gets an enormous amount of use. Allow me to interpret this, " I can't answer your arguments about: John 6, Romans 9, Ephesians 1, Hebrews 7:23-25, Acts 2:32, Acts 4:28, Genesis 50, Isaiah 10, and Isaiah 46:8-11. So I will accuse you of idol worship." Calvinists don't believe that Calvin saved them. I don't quote from Calvin's institutes as inerrant scripture. I do believe some of the same things that Calvin taught especially about soteriology, and so did Luther, Augustine, Spurgeon, Edwards, and others throughout church history. Along with them I also don't agree with everything that Calvin taught. The title Calvinist carries a lot of baggage. Largely this is due to misinformation and misrepresentation. Calvinism means you believe a certain set of propositions concerning Christianity, and none of those propositions entail Calvin worship.
Another one is "hey, you're into theology and I'm not". Everyone believes something about God, especially Christians. Christians read and study their Bibles; they listen to their pastors. All of these are ways of studying God. All Christians are theologians, the only question is: are you a good one? A huge problem in the western church is, as Dr. Greg Bahnsen puts it, "anti-intellectual pietism." There is this idea about studying theology--that it is this dry, non-spiritual act. What most Christians today are really seeking after is an emotional experience, if something doesn't feel good or fair then it must be wrong, and if you think too much you are going to miss the point. Does this mean that we should think less? Is this really the message of the Bible? Or is the message of the Bible to have Christ as Lord over everything, even in our realm of thought; to have Christ as Master, as He has revealed Himself--not how we want Him to be. That is why this issue deserves so much attention; because fundamentally what we are talking about is, who is Christ? how has He revealed Himself? It totally distorts who Christ is if we sacrifice truth for some kind of illusion of unity, which is exactly what unity is if there is no foundation of truth.
The ultimate reason why debating Calvinism and Arminianism, monergism and synergism, is divisive, is because one side strips man of his so-called "autonomy", and emphasizes man's fallen nature. One side has God on His throne doing what He wishes with His creation (Isaiah 46:8-11), the other has God waiting desperately for man to turn His key because God has already turned His. One side has God saving perfectly (John 6:37-44), the other has God trying but failing to save. If you believe that salvation depends ultimately on your "free will" decision for God, then that will affect your life. What you believe about God has a huge impact on the way you: worship, tithe, pray, eat, breathe, live, you name it. Believing that God saves sinners by Himself, and not after you allow Him, will change you. Theology matters.