I was raised RC but gravitated towards TEC in my later teenage years. I especially found my way to Anglo-Catholicism, after brief stints in various liberal yet liturgically-traditional Old Catholic and Independent Catholic movements. I still also have no qualms about the Liberal Catholic tradition. For me, the most important matters are Liturgical, and the RCC in America has largely dropped the ball on that. There is little dignity in the typical run of the mill NO Catholic mass. Ho hum priests, ho hum liturgy, mediocre music, no incense, no processions with all the pomp and dignity seen among the Anglo Catholics. In NYC, after checking out the Latin Mass at St. Agnes, where they do a lovely liturgy, I found my way into St. Thomas, Resurrection, and the infamous Smokey Mary’s, and absolutely loved it. I found that this afforded me a way to embody progressive faith while remaining tethered to Catholic tradition, as TEC seems to value things I do (Reason as a pillar of faith, in addition to Sacred Tradition and Scripture, a distinctly non-authoritarian and democratic approach to decision-making, interfaith spiritual collaboration, tolerance, etc., basically all the things many right-wing Anglicans believe are to blame for the demise of TEC in America), within a more established denominational milieu. (Independent Catholicism is still a free for all).
In brief, I’d say that for right wingers, perhaps Rome offers a more welcoming home to support them in their views on sexual politics. But there are also those who found themselves estranged from Rome due to a simultaneous sanctification of right wing sexual politics, and a very sad denigration of the glories of Tradition.