This may be a reflection of my preferred sources, but I don't think anyone on the right, individually or collectively, even if they are considered an influential person, has the power to cancel anyone on the left. Whether they can cancel anyone on the right is a an interesting question. Similarly, people who one would think fairly invisible and low on the power scale - college students, state legislators from thousands of miles away, minor journalism figures - have the ability to cause trouble for conservatives and centrists, and even liberals at times. This unbalances discussions that should be carried on even-handedly, and causes conservatives to look more defensive and strident than they otherwise might.
That is a subtle but real debate advantage that otherwise decent people on the center-left might not realise they have, which can be parlayed into emotional and social advantage because of the increased freedom to use quiet virtue-signalling and condescension without getting called on it. I am thinking of a church debate in which one person started out by saying that he thought the opposite position was "unloving." The specific examples I can think of in that argument are heavily weighted against him, yet he can say that and his opponents cannot without having to engage in a tedious and rather irritating rebuttal that would work against them in persuading a crowd.
Leaders in organisations can give an appearance of being generous by allowing conservative views to be expressed at all. Yet they are nearly invulnerable in expressing their own view. They are being generous with little cost. There are certainly places one can go where a general conservative view is expected, and liberals might feel they were being invalidated and looked down on. That is not a good thing. But they are in no danger of losing their job over that. Someone might laugh at you or treat you with scorn. Well, welcome to my career for forty years working with liberals.
Maybe it's different in Utah or Alabama. I live in a bubble as well and may read the signs wrongly. But I don't think social workers get censured for having views more liberal than average, nor denominational pastors, nor academics, nor government employees, nor any profession that depends on a public image. Rarely, they might get into trouble for actions which are more leftist than their organisation has chosen to go. But I don't think you get cancelled for those opinions. In some places, you see yourself as just waiting a few more years until your crowd takes over.
As I said, I may be missing an entire category of situations where this imbalance is not true, or even reversed. I am glad to have a go at considering what those mean. However, they are not easily coming to mind.