I hope that, by "giving up," you mean to quit your job and nothing else.
Workplaces (especially those provided by small businesses) are really just a never-ending version of high school. You have the cheerleaders, the jocks, the brainiacs, the geeks, the nerds, the rich kids and the principals. We all know that is true. The gossip and insults are exactly the same.
So, should a person who is left holding the short end of the stick "give up?" I have done this and found new (and friendlier) employment quickly. But, it is always a risk without a guaranteed job before your money runs out. Instead, try looking for new employment now while you still have your job. Quit only IF you accept a job offer.