Is it important that we win the hearts of theists?

It seems that atheists often engage with battles to try to win over the minds of theists. However, many theists, particularly the non-sophisticated ones, operate more on emotion than logic. This is why I think it's so unfortunate to see many atheists certain groups like theists or creationists as "idiots", "retards", or other certain terms I can't use on GameSpot. Not only does this repel theists from atheism, but it also devoid of any logic usually, substituting passion for reason. It's very often I see that an atheist will simply remark how ridiculous a claim may be, without giving it much thought it appears, as though they're perfectly content with analyzing it from the surface only.

I think atheists should be respectful of theists, so as long as the theists do not pose a threat to their safety (which in most cases, they don't). Calling them a bigot because they don't accept same-sex marriage or think atheists shouldn't be allowed to hold office is not helpful. We have to base debate on understanding, not hostility. If we focus on hostility, we'll never get the opposition to understand us and they will likely continue to be an enemy.

Am I alone here or has anyone else noticed elitism going on with the modern atheist movement? It could be that I'm talking about the non-sophisicated atheists, but it seems that atheists in general are more bitter than theists.

I obviously come from the other side of the coin.  As such, I see this question from the opposing perspective.  That being said while I do see many atheists responding in the manner you describe, theists themselves often treat atheists in a like manner.

Many evangelicals quickly quote Psalm 14:1 which in part states, "The fool says in his heart, 'There is no God.'"  However, given the context of the statement it is my understanding that this is speaking of everyone, not merely those who claim to be atheists.  The rest of the statement, after all, does state, "They are corrupt, their deeds are vile; there is no one who does good."  Would not this mean that every individual upon the earth in some manner rejects the notion of God within their heart?  All - theists included - have fallen short of the glory of God, not merely atheists.  This is something I think many Evangelicals such as myself have forgotten.  

Let's not forget that if one claims to desire that he wishes all to know Christ, in what manner is calling the atheist a fool for his unbelief an effective evangelism method?  All are at once in unbelief, not merely the atheist.

But to go back to the original topic, I agree that we should all be civilized in our discussions.  To use your examples, name-calling and forcing those within government ideals to hold to certain beliefs is simply not how a multi-religious nation should behave - regardless of what position one holds on the topic.  There should be no religious nor non-religious requirements that we must have for the commander-in-chief or the common person on the street.  Certainly we can and should discuss and seek to put forward our positions (which I wish to devote my life to btw) but live and let live.

That is a hard question to answer because you cannot paint all theists with the same brush. The majority of theists genuinely believe what they are saying and generally try to live out good lives, helping people around them. If that kind of person is engaged in a discussion about the nature of the universe they will more than likely present what they actually believe in a respectful and friendly manner. These people, like every other group run the gamut from dumb to intellectual. Treating them poorly because of their belief would be wrong and, indeed, counterproductive (Assuming the atheist in question has some objective in mind) 

The problem is that there is another, much smaller group of theists who don't ascribe to the idea of amicable discussion and friendly exchange. These apologists, often hold dubious degrees in "science" or philosophy and rely on parlor tricks and rhetorical smoke and mirrors to "win" the discussion. They are not interested in respectful discussion, only in the advancement of their position. They often ridicule their opponents and claim victory regardless of the outcome of their exchanges.

Consider this podcast as an example. (It is from a blog called Tuesday Afternoon.) The format of the podcast is to invite someone who has an interesting idea concerning one of the subjects the blog covers and have that person outline his position. Vary rarely do the producers critique or dissect the position of their guest during the pod cast. In the episode I linked, the guest knows this, but uses the show as a platform to propagate his idea. He relies on deeply flawed arguments to advance his position (Knowing they won't be critiqued) and then acts as if he won a debate which he wasn't even having. This kind of behaviour is not respectful, so why should anyone respect it? This man is a charlatan, and there are many like him. Concerning that kind of theist, no I don't think they should be treated with respect. At most they should be dismissed as the frauds that they are.         

Zealous theists may appeal to emotion often, but they still employ reason in their arguments, whether their judgments are sound or not.