I’m married to an evangelical Anglican, and it works very well. On the other hand a former Catholic coworker married a baptist girl whose father is a baptist preacher. He bought into it hook, line and sinker.
They are divorced since many years. We are still married since 28 years. YMMV.
One thing that will sink the relationship for sure though, are apologetics and doctrinal arguments. This kind of relationship requires great maturity. If anything, focus on your common love of Christ, and leave the other freedom to seek Him in the way each knows best. Pray for each other a lot. Evangelize not with words, but with acts: remain true to you faith and devotions, and always act with Catholic charity, seeing Christ in your girlfriend, and her father. When they try to engage you into an argument, don’t bite, but do answer any questions as best you can.
Two examples: once my late Pentecostal mother in law admonished me to pray the Psalms as we sat on the balcony on a warm summer evening. I had just finished reading Vespers and my breviary was still beside me. So I showed her what it was all about. Next thing you know, she was attending Vespers with me (in Latin!!!) at the local Abbey. She didn’t convert before she died, but I never again heard any anti-Catholic diatribes. She’d just ask genuine questions on our approach to faith, but never argue.
Another time I was standing outside the abbey on a warm evening waiting for Vespers when a “bible-believing” Christian started railing about how monasteries were the work of men,and not God, not in the bible, etc.
I replied “I see you love the Bible as I do. Have you ever heard of Lectio Divina?” He hadn’t, so I explained a bit what it was and encouraged him to Google it.
Plant a seed, not an argument. Faith comes from the heart, and some measure of self-discovery, and a planted seed.