"For" is not the best word to use here. I would say "despite" or "given". The sentence means that EVEN THOUGH this person makes a lot of noise, she does not like to express her feelings.

I think calling this usage “not best” or “literary” overstates things a little. I think it’s a use that is falling out of fashion, but still in use, especially among older speakers. “For all her efforts to get her Dad to wear his hearing aid, he came to the dinner without it and didn’t hear a single conversation. “ “I noticed that you spent a lot of time working on your vegetable garden.” “For all the good that did. What the rabbits didn’t get, the deer did.”

James has given a good answer. I just wanted to add that this usage of "for" is literary. Nobody uses it in speech, but you will sometimes see it in writing (particularly in older texts).