Being shomer negiah is a very important halakha. I am not Haredi, but my Judaism is defined by halakha, and the moment you pick and choose which halakhot you wish to keep and not keep, you’ve effectively separated yourself from the Torah and might as well be Reform- the Reform Movement believes that the individual and the individual’s definition of truth are the supreme authority, not the objective Torah. Relativism may be a popular 20th century value, but it is the antithesis of Judaism.
This girl sounds more frum than you. She needs another baal teshuva, and I will explain why.
People need to be with people who were raised similarly. She cannot relate to your formative experiences in life and you cannot relate to hers. You were raised with a different value system than her, and her ideas of family are also different than yours. Her family will think you’re a frummy, and that you’re weird and your family will never fully accept her. They’ll never view her as equal and will be skeptical and judgmental.
Don’t subject yourself to a lifetime of heartache and machlokes. People not raised religious have a tendency towards zealotry and even fanaticism when they become religious because they lack a social lens and an experiential lens through which Judaism is lived, beyond the printed page. This seems to be the case here.
You sound like you need a girl who was raised frum and maybe became more relaxed over time, since such a lukewarm girl can relate to your hashkafa of seeing halakhot you don’t like as irrelevant.
The BT girl should seek another BT who is frum and shtark, a guy who maybe went to Aish or Ohr Somayach and who consciously made a choice to be a halakhic Jew and doesn’t go with the flow because that is how he was raised.