I really dislike my girlfriend's partner - how do I feel compersion?

When I started seeing my gf she had just gotten out of a mono relationship and her ex was extremely mean to her after the breakup and I was there for her. Recently they have started a romantic relationship again and it is like all of that didn't even happen. My gf knows that I don't care for her now-gf because of that but I want her to be happy so I don't make a big deal of it. So my question is how can I feel any sense of compersion when all I have is negative feelings towards her?

It’s typically an exercise in futility to try and force yourself into a feeling you don’t have. You don’t need to try and conjure a sense of compersion or a feeling of goodwill about this person who you have every reason to dislike. 

It sounds like you’re doing everything right here - not “making a big deal of it,” letting your partner make her own choices, and just sitting back and staying disengaged from a situation you find irritating and frustrating. 

Try to re-frame this as not being about the metamour, but about your girlfriend. She is making a choice that she thinks is best for her, and all you can do is support her in that, recognize her agency, give her space to make her own choices. Sometimes people we love do things that we wish they wouldn’t. Sometimes they make choices that we think are bad choices. But that’s the beauty and the aggravation of having relationships with people. They insist on being their own people and doing their own thing even if it means refusing to quit a job that clearly makes the miserable or dating someone you don’t think is right for them.

And you seem to have that pretty well figured out - you’re leaving her to make her own choices and figure her own stuff out, without adding pressure or ultimatums or futile cajoling. Give yourself a break for not being able to feel thrilled and excited about this situation. If it starts to negatively impact you, set the boundaries you need to set; otherwise, no one can really fault you for only being able to achieve a sort of detached neutrality at best about this person’s re-entry into your girlfriend’s life.