Let's see if I can explain this in a suitably a-religious manner...The people to whom it matters dislike those with atypical sexualities, and they want a reason to persecute them. It is a lot easier to persecute someone for making an immoral/disgusting/wrong choice than it is to persecute someone for something they have no control over. Thus, the seek out explainations (or sometimes, they don't seek, and just stand still shouting it as loudly as they can) that support sexuality being a choice, so that they can continue to call it "wrong."
If it's not a choice, then those people are forced to think about why such people exist in the first place, and whether it's truly immoral, and thus okay to persecute. That's how I see the whole discussion.
SpoilerIt is important to note, of course, that not all of the people who feel that whether sexuality is a choice or not feel that way because of strong religious convictions. It's just that, in America at least, that seems to be where the most powerful and vocal of those who think that way approach the issue.
It's also not to say that all of those with religious convictions find it abhorrent; I would call myself very religious (or spiritual perhaps, because I don't follow an organized faith, but a personal mish-mash of the ideas I've found to have the strongest ring of truth; but that, I suppose is for another time and place), and obviously I have no issues with the idea .