I'm not going to forgive my mom for being transphobic after somebody influenced her
What makes you think your mom is transphobic?
I heard my mom say transphobic things in front of me.
Rather than fight with your mom, it's a good idea to just refuse to fight with her and shut it down. You won't change her mind and she's still entitled to her opinion at the end of the day.
I've tried, but I want her to know that I disagree with her opinion.
It's natural that sometimes family members have opposing views on sex, genders and politics. If its that important to you then you should try approaching her calmly and keep the discussion from escalating. She might even come around to your point of view.