It may or may not get them fired, it would depend on the severity of the situation.
If it was being mouthy and obnoxious to a pilot, it would probably not result in termination. A stern talking-to and a note in their file, yes, but not termination, at least for a first-time offense. However, if it was a
safety issue in addition to being mouthy, doing something flagrantly against regulations, it could result in being fired, especially if said individual was still on probation.
I do believe in CAs removing F/As from flights if there is an attitude/authority issue. Believe me, I've seen some massive 'tudes that really needed checking. Sad really.
I wish that we could all just get along and respect each other and each other's jobs.......
Flight attendants unions have professional standards committees just like the pilots' unions do. If you have an issues with a F/A, please do bring it up to them. The contact information can be found on places like bulletin boards in the F/A crew lounge areas, even the inflight supervisor's office.