As far as dogma, am I compelled to support bans on abortion, contraception, and LGBT relationships in order to be a good, practicing Catholic?
We are to be against abortion. That can take various forms, for some of us it means working to build a community where no woman every feels abortion is her only option.
For others they feel that work needs to be done politically.
The US Bishops have written a wonderful guide
This goes to the heart of things, the very basic line is imagine there are two candidates.
Sally Smith and Joe Jones
Sally Smith talks about “Pro Life”, yet, she is pro-war and believes that there should be no regulation on pollution.
Joe Jones says he is “Pro Choice”, yet he has stands on economics, war, wants to give parental leave to all parents, wants to increase opportunities for the disabled.
You may vote for Joe Jones over Sally Smith as long as your intention is for his stand on the other issues. You cannot vote for Joe Jones if you are doing so only because you hope he will make abortion legal at a Kiosk inside every mall. (Using hyperbole here to make a point).
Contraception is no longer illegal in the US. I have not heard of anyone pushing laws that would reverse Griswold v Connecticut. I doubt such a law would get even one supporter in Congress, or in any State legislature. You are pretty safe on that one.
Again, like Roe and Griswold, this is now established law in the US. I don’t think there are going to be laws presented to overturn in the US in our lifetimes.
We are called to love everyone, even gay or trans people.