First thing I would say is to start the process of becoming Catholic doesn't commit you to anything. So you can do the whole RCIA course (either individually or in a group, depending on what your parish does) and there's absolutely no pressure to be confirmed as a Catholic at the end of it. It's a great way to have a decent space for all your questions and thoughts. I think it's very healthy to come along while you're still considering it and have doubts, some people want to have everything 100% sorted in their heads before beginning the course, but that's exactly what the course is there for: to help you reflect and work out where you stand.
Secondly, I've found over the years (cradle Catholic although I've experimented with various other denominations in my youth, now work for the Church) that a lot of the moral issues, especially the ones that are counter-cultural around chastity and sexuality for example, made sense from the inside once I chose to live them, but not when it's an intellectual argument in my head. So I used to contracept and couldn't see what the problem was with it, but eventually decided to accept Church teaching and use NFP, without really being convinced that it was the right thing. But then once I was using NFP, I saw what a difference it made in my life and relationship with my husband (which still, unfortunately, fell apart, but not because of that) and became convinced of the wisdom of the teaching.
And thirdly, some of the social issues may not be as big a deal as you think. We spend a lot more time thinking about the Trinity than we do about other people's sex lives! As you saw from the CST formation, the Church can be quite 'left wing' (although it wouldn't fit into the terminology of left and right as it's used in everyday speech, with 'left' being used to mean 'socially liberal'), certainly economically and on a lot of issues. On an everyday level, even most Catholics who are fully signed up to Church doctrine on every issue (which is by no means most practising Catholics) wouldn't pressure people who aren't Catholic to follow Catholic teaching, e.g. you would be hard pressed in the UK to find anyone who would have anything much to say about a gay relationship between two non-Catholics. Obviously it's different for people who are Catholic, and then there's a lot more diversity of opinion. With abortion, I don't know anyone who would judge a friend, or even a stranger, who had had a termination. Even quite stauchly pro-life people know that it's often a near-impossible decision to have to make and have every sympathy for women who find themselves faced with it. There's a lot of training for priests and people who work in the Church in pastoral ministry, every conversation is personal and considers the individual circumstances. Personally, I like the fact that the Catholic Church has very clear teaching on a lot of issues, but it is always balanced with a pastoral sensitivity for the case in hand. That's why some people are moral theologians and different people are parish priests, it's not the same skill set at all!