This is my opinion:
Both A and B are correct.
You could also correctly say:
“In modern society, clothes do more than TO just keep us warm.”
Perhaps B sounds a little weird, but that doesn’t necessarily make it incorrect. Whether or not something sounds weird is often a matter of personal preference.
If Steven Larrabee can provide an argument for why B is incorrect I will accept it, of course. But so far he hasn’t really done that in my opinion, only stated that he doesn’t like it.