This seems evidently false. Some examples of such organizations are By Any Means Necessary and Refuse Fascism. Both are formed by various anarchists, Trotskyists and other radical (in the sense of wanting to radically change the current organization of society) leftists. Both fight against Trump administration and for LBTGQA+ rights and various forms of socialism.
Given the large numbers of people involved you can probably find a Tweet that somebody twote that was a policy violation and didn't result in a lock.
What about that?
As for whether the post should be removed.. well, I’m personally against censorship, but if you’re going to remove Trump’s posts then I similarly think this post ought to be removed as well.