What's the proper term to use if you want to talk about trying to move up in the lineup or switch up?
As badroit notes, queue is more common in British Engish whereas line is more common in American English in non-technical settings.
A queue-jumper cuts in line, in which cut may be interpreted as the sense of trimming or dividing depending on whom you ask; Merriam-Webster lists this sense as a separate meaning:
cut: intransitive verb 5. to advance by skipping or bypassing another. cut to the front of the line
To butt in is to intrude. In queueing cultures, cutting in line would be rather rude, and could be described as butting in into line, especially if one is literally physically butting, i.e. thrusting or pushing headfirst.
Bud in is probably an eggcorn for butt in.
I'm here because I just heard Rainn Wilson say "butt in line" in the movie Super. I grew up in New England and I'd literally never heard that phrase before. We say "cut in line" and have said so since I was growing up in the 60s. Usually, you just say "Hey! No cutting!"
SO, who grew up in New Jersey, says it was always "cut" there as well.
I’m from Upstate New York and we would always say ‘no budging’.