Advice for Catholics
There's lots of advice I might have for Catholics that they're not going to take (e.g., becoming even more traditional than The Society of St. Pius I), but there's one piece of advice that might make a difference:
Keep clerical celibacy.
Under normal circumstances, a large organization will drift left. That shouldn't surprise anybody. A large, powerful, and prestigious organization is a much bigger prize to people who want to tell others what to do than people who don't.
The Catholic Church has been one of the few exceptions to that rule. I suspect that's largely due to clerical celibacy. In eras when clerical celibacy is taken seriously, it will keep out those more interested in the office than in the duties of the office. (In eras when clerical celibacy was ignored, e.g., the Renaissance, the Catholic Church was more inclined to abuse its power.)
If the Catholic Church gives up clerical celibacy, I recommend that Catholics brace themselves. A two-Pope system may look preferable.