Except in rare cases (I can think of 2 where I think the person sincerely meant that she believes God loves me and she knows we don't agree on religion but there wasn't much she could do except offer her prayers), it bothers me, too. More often than not when I have been told God loves me it is NOT a nice thing to say, they don't mean well, they mean they think I'm too stupid to waste their time on. I feel like it's kind of condescending, like they have some magical secret that they're trying to let you in on.
It's also rude because it's dismissive; 3 words to negate anything you might have said. "It doesn't matter that you have logical arguments to the contrary, I know better and God will love you anyway." Gee, thanks. Plus another aspect of it being dismissive is that it almost forces their religion on you, i.e. no matter what you think it's ok, God loves you even though you are wrong.
Also it bothers me because it's intellectually lazy, the easy way out. "You're an idiot, but God loves you and I don't need to actually try to do any work now."
That is all. For now.