It happens to me a lot because (apparently) I'm not intimidating enough for people to not-dare cut in front of me. Or maybe, because I come across like "a nice, little, 'nothing-in-particular' lady", people make the mistake of thinking I won't mind their going first.
In any case, I get aggravated when it happens (particularly since, after an adult-lifetime's worth of people seeming to assume I won't mind, seeming not to think they're apparently more important than I am, and/or seeming to think that being aggressive and rude is the only way to get through life).
So what do I do about it? Nothing, really - except to make faces when it happens. If I'm with someone I'll make a face (and maybe a remark) to the person I'm with. If I'm alone, I make make my "disgusted face" at someone nearby who noticed what happened. If there's nobody around who saw it, or who'd see me making the disgusted face, I usually resort to evil-eying the back of the head of the guilty party (sort of hoping, I suppose, that my eyes have some kind of "melting power" that will - even if they don't really melt - make them feel squirmy.
Sometimes, a person who "cuts" doesn't really seem aware that he did it. He just didn't notice that I was there first. Sometimes, too, there are people like struggling elderly people who are so wrapped up in their own struggles to notice who else was in line before them. None of that kind of thing makes me angry, and I usually kind of laugh it off. It's when someone knows he's being aggressive and/or acts arrogant that I get angry.
I'm not the type to get in a fight with people. It's not how I want to live my life. Besides, those people who think I"m a good target to cut in front of are essentially right: I don't do well in verbal confrontations because I don't do verbally well when people are unreasonable. Neither would I do well in a physical confrontation because I'm not aggressive and nasty, so I lack "killer instinct".
BUT, if I think someone has treated me in an aggressive way and/or taken advantage of me because I'm obviously not a "killer instinct type" person and obviously unlikely to be a rude or hostile person; that makes me mad. I'm not about to just laugh that off. If nothing else, my "disgust face-making" and "sending of melting eye vibes" gives me the feeling that I'm at least expressing my contempt and disgust for how I've been treated. It isn't much, but I think it's better than just happily taking it and doing nothing.