Been bouncing this around in my brain for a while, but @luckthebard 's recent post about anti-sex movement in Progressive circles made something click for me.
In actual-play fandom spaces, the same people who yell "it's their table, let them have fun" if you point out structural, story issues, are often loudly anti-sex, anti-violence, or anti-conflict about the same stories.
And the irony is, it's way more appropriate to say, "it's their table" in response to anti-sex etc. criticism than it is to direct it at story criticism. Because shows like CR and D20 have made their style of humor and relationship with adult content extremely clear for the last decade or so. To wade into their space and demand that they change their table culture and brand is ridiculous.
But it makes sense that both the anti-adult content and the "it's their table" demands are coming from the same place. Because both come from a desire to police and control the behavior of others.
In my experience, people who criticize actual play storylines aren't trying to change them-- they're processing and commenting and discussing what works and doesn't work in a given story. The people wading into these conversations to say "it's their table" want to shut the critics up. They don't want to join the discussion, they don't want to block and move on with their lives. They want everyone to either share their opinions or be silent.
Likewise, the anti-adult content crowd doesn't want to Listen to Re-Slayer's take or DesiQuest or one of the countless other actual play shows that has a table-culture more to their liking. They want Critical Role and Dimension 20 to fit into their box of comfort.
So instead of curating their own experiences and taking responsibility for the things they consume, they get moralistic and try to force everything around them to fit with their beliefs, opinions, and taste.
Which is functionally authoritarianism in a progressive hat.