take sides

take sides (to choose one side of a disagreement to support) — принять чью-л. сторону; встать на чью-л. сторону; поддержать кого-л. (одну из сторон); примкнуть к той или другой партии

When two people you know have a disagreement, you have two options. You can stay neutral or you can take sides. If you take sides , it means you choose to support one person over the other. It can be hard not to take sides if you believe one person is right and one is wrong. But if you want to stay on good terms with both people, it’s better to stay neutral. (EB)

Example: She didn't think it was wise to take sides in their argument. (OALD)

Example: The boy was careful to make sure he didn't take sides in his parents' divorce. (EB)

Related vocabulary:
side with
stay neutral — соблюдать нейтралитет; не принимать ничью сторону
change sides — перейти, переметнуться на другую сторону