In terms of “what is a conservative Catholic”, I’d rather avoid the term. I try to be an orthodox, practicing Catholic, in union with Pope Francis and my bishop. I know people who say they are conservative or traditionalist, in the sense of rejecting Vatican II. Other people in the 1800’s called themselves “Old Catholics”, rejecting the Magisterium in their generation. There were other groups before that, and will be others in the future.
The terms liberal and conservative are misleading when taken from politics, and applied to Christianity. I have opinions about many discretionary subjects, on politics, economics, and other matters, that could be classified as liberal or conservative. Your opinion is as good as mine. I object to people using the parish church to promote opinions on discretionary matters, even if I sometimes agree with those opinions. My former parish allowed people to use the parish to push any opinions they wanted; one time at Mass they pushed an announcement urging voters in the school district to vote “Yes” on a special ballot to raise taxes to fund the restoration of German instruction in the public high school, which had been cut due to budget problems. Every week there was another opinion. The parish also allowed prolifers to mention, one week, that abortion is also a concern - every group, every opinion got equal time at the microphone. The parish eventually closed.