Or they have a third reason, like that they think their religious views happen to be true but that whether they're true or not doesn't actually affect most people's day-to-day lives, and they don't think it matters if you believe the same as them.
Oh to be sure, such religions exists. For example, most classical forms of Judaism believe that non-Jews aren't obligated in the 613 commandment. But, that still means that not convincing people is letting people remain fundamentally ignorant about extremely basic aspects to the nature of reality. That's not cool.
But note that even then, there are clearly people who aren't doing that. Consider for example, how many evangelical Christians there are who believe that people who have not accepted Jesus Christ as their personal lord and savior will burn in hell for eternity. How many of those slack off and aren't spending most their time trying to save us? They claim to think that the consequences of not believing is eternal torture. How can that not matter?
And why do you want to convince people when (you think) they're wrong?
A variety of reasons. First, I intrinsically value truth. Second, in general, humans will do better having a more accurate understanding of reality (there are likely some exceptions to this but the general pattern seems clear). Third, (connected to 1 and to 2) I'd like to live in a world where people do try to correct each other when wrong (this also has a selfish element. If I live in such a world, then I get to be corrected when wrong.) and by trying to convince people when I think they are wrong, I am contributing to making the world more that sort of world.
Oh to be sure, such religions exists. For example, most classical forms of Judaism believe that non-Jews aren't obligated in the 613 commandment. But, that still means that not convincing people is letting people remain fundamentally ignorant about extremely basic aspects to the nature of reality. That's not cool.
To their credit, I suppose, the Lubavitcher Chabad people are promoting a Noahide movement for us gentiles, of which I'm sure you've been made aware. This movement has some interesting implications. For instance, I have a book in front of me ...
I have noticed during my dialectic adventures on the Grid that religious people, no matter how "reasonable" (i.e. moderate, unaggressive, unassuming, gentle, etc.), would get very annoyed by an assertive, dry Atheist perspective, which they tend to nickname Hollywood Atheist (interestingly, religious people tend to use this term to atheists that openly make fun of religion and are very assertive and even preachy about their disbelief, while atheists tend to use it to mean people who are atheists for shallow, weak reasons and who do a poor job of defending their stance in an argument). There is also the tendency to compare the certainty of an Atheist with that of a Fundamentalists, when they are fundamentally different in nature (pun unintended), something they do not seem to be able or willing to grasp. Not that atheism hasn't had its fair share of fundamentalists, but that's supposedly the difference between an atheist who is so out of rationalism and one that is so because they hate the Church or because Stalin (glorified be his name) told them to.
On of the things that irritate them the most is the phrase "God is Dead". A phrase that is obviously meaningless in a literal sense (although, of course, God was never a living being in the first place, by the current definition). Figuratively, it means something akin to "Our Father is dead": we are now orphans, adults, we don't need a God to tell us what to do, or what to want, or how to see the world: we decide for ourselves, we see for ourselves, we are now free... but it does feel a bit lonely, and, for those who relied on their God or Parent Figure as a crutch, it can be hard to adapt to a world without a reference, without an authority figure. A world where you are the reference, you are responsible for your own moral choices.
There are other things, specific arguments, methods of approach, that anger them and are counterproductive to the submitting of the message. Of course, the atheist message is a Brown Note of sorts to the religious mind, since it challenges their entire worldview (though in the end it all adds up to normality... except much more seamlessly). However, it would be nice to develop an approach towards theists that avoids the frontal part of their mental shields and gets into the seams, using the minimal force in the points of maximum efficiency, bypassing their knee-jerk defences...
So, here is my question to you all: how do you get your points across to a theist without pushing any of their Berserk Buttons, without coming off as a condescending and dismissive jerk, and without having to shorten all of the freaking Inferential Distance?
Developing a general algorithm would help us spread our ideals further, which, as far as I know, we think will be to the benefit of all humanity and might in fact help us avoid extinction. So, suggestions...