Or, just quit. I've taken conflict all the way through being fired multiple times and there really isn't a way to win if you are not part of the mafia. At a very huge ecommerce company they had SDE career training, and you are told bluntly all the people deciding things are cigar smoking mobsters so basically, you are a peon and you're fucked for a career if you are not in management. You need to enter a company through personal connections not skills, or it just isn't going to work no matter how much politics you try.
There are tactics I call socialist tactics. Many people for instance being on the losing end of an argument having a dumb idea or no clue, will use their position as a management to call a large meeting, confuse all the people in it with bullshit, then get them to agree on something they don't understand. Another tactic is when challenged in a meeting, call for a instant vote (its a democracy) while pressuring people to vote for them. Third tactic is to meet for a few hours, decide everything you want, then try to force teammates into the meeting two hours later, then claim the whole team is on board with what they decided because everyone was in the meeting. Fourth tactic, is to lie continuously and whoever is around upper management the most/most face time wins with the most lies.
I don't condone any of these, but shitty managers will use all of them and they seem to be learning them somewhere because I see them repeatedly.
Perhaps the best advice for your situation is to praise publicly, criticize privately which is also what a lot of office bastards do all the time.