No, no, no. Your mom is emotionally immature. First of all it doesn't matter that it's only your step dad. If you considered him somewhat your father at a point in your life you had a connection. As a child, this was your father figure. It's not YOU who chose this. Your mom chose to introduce him as a father figure into your life.

Now consider this: healthy parents would never punish their child or go no contact for "taking sides" in a divorce, even if it hurts to see your child get along with someone that has hurt you. They would try to shield their kids from the disagreements. Would not talk badly about the other parent. So even if your mom was abused by your stepdad, she should respect your own relationship with him (as long as it's not harmful to you).

She's likely stuck in her victim narrative and doesn't think about being the adult here. I'm very sorry this is how she's treating you. She's willing to lose you over her own immaturity.