Your first point is well taken. I stand corrected. “Many” members. I’m not sure what you mean by theologically constant. Is not faith ever evolving? The Vatican has a good many theologians and biblical experts always at work. They are adding to the faith presumably. Are you really saying that there is never a correction in any doctrine because the RCC claims it cannot error ever? I’m not sure, so won’t go further.
What I mean by socially more liberal, is that I find the RCC, and please correct me if I am wrong, taking a strong position on protecting the immigrant especially in the US. It has at least through it’s Popes made faith strong statements against the death penalty and war in general, not inclined to find just war. I think that whatever you think about Liberation Theology, the RCC has acknowledged that the Latin American peoples have suffered unjustly for decades under dictatorship, and it has endorced a “preferential option for the poor.” It seems to be moving rather to the left on issues of the environment. I see those as “liberal” notions.
Theological liberalism to me is a willingness to offer up the best analysis to date. I think the RCC, and this is surely my opinion, drags its feet on even what is produced by Catholic theologians and biblical experts which differs with historical claims by ECF and councils of centuries past. I assume this comes from “no error” can be possible by us.
I also think, and again, it is an opinion, that some statements in the past are now clearly wrong and and thus the RCC is somewhat hesitant to make any statement now to the contrary until “all the evidence is in.” Being burned as it were on the Galileo issue (I realized that some RC’s now dispute this, but the Pope did in fact apologize), the Jewish issue (again another apology), and evolution seemingly proven even to Vatican satisfaction, causes it to be reluctant to speak until they are 99% sure of being correct. No doubt some RC’s would disagree. But you asked my opinion.
SO in the end, I find the RCC theologically conservative in that sense, and socially liberal.