Worst case scenario...
My boyfriend's wife has a lot of hostility and prejudice towards me. Tommy, our shared partner, doesn't talk to us about each other. She and I only interact at parties. We used to try and communicate via text and email, only to find it created more problems. There's still tension but we've set new boundaries and everyone is in an okay place now.
My best advice is to keep it superficial. If you don't like this person, don't force yourself to for your partners sake. Let their relationship be separate from yours and don't stir the pot unnecessarily.
I'm Alberta (F/26) and I've been in a relationship with Doug (M/37) for 3.5 years. We are long-distance and open. For the last 9 months I have also been dating Tommy (M/31). Tommy is in an unconventional marriage with Jordan (F/28).