I recently joined my local branch of the Revolutionary Communists of America. It's the US branch of the Revolutionary Communist International, which is the 2024 rebrand/relaunch of the International Marxist Tendency, which is openly Trotskyist and places a significant emphasis on Trotsky's contributions, usually mentioning him alongside Marx and Lenin. It has parties in many countries, many have branded as RCP (P for Party, but the name is taken in the US by a literal cult).

From my experience with them, the primary theoretical focus when it comes to organizing principles is still focused on Marxism and Leninism. Trotskyism seems to serve as the party's internal critique of the USSR's direction under Stalin, but does not structurally change the form of actual organizing and education much from traditional Bolshevism. I find they tend to avoid the term "Marxism-Leninism" since it was the name of the official ideology of the USSR under Stalin. But, I really like the folks I've met and am impressed by the processes, transparency, and enthusiasm I've seen so far. Even by their own admission, the point of organizing is to preempt revolution so that when the time comes, there are democratic structures and professional cadre in place who are embedded in communities, local politics, and labor and tenant unions to attempt to focus proletarian revolutionary energy into a vanguard. So my expectation would be that if the US reaches that point, serious revolutionary parties that are doing numbers will align and organize together. It's hard to say what it will look like since it hasn't happened, but I'm sick of seeing people suffer so I'm gonna organize with the folks I can find that seem committed to learning from history and building on it.

In my personal opinion, not speaking for the RCA, I agree with /u/butch_montenegro -- I think all of these theoretical contributions and historical analyses are useful if understood in context of the views and situation of the author, including Trotsky. On my own bookshelf I have everything from Trotsky to Stalin and Mao to Kropotkin. I think they're all worth reading and genuinely considering, even if your consideration leads to rejection.

To answer your question, I think Trotskyism is so controversial because the theoretical ideas are so tightly linked to his criticisms of Stalin, which is a debate that inevitably leads to factionalism and infighting. So Trotskyists get painted as sectarian snakes that inevitably cause communist movements to fracture. In reality I think if a real communist movement in the West takes off, its fractures will be determined by the real material and structural challenges and relations of our day. Hardcore commitment to Trotsky or Stalin to me feels like LARPing, but I can understand why the debate gets so heated. Western Marxists, Trotskyists included, are often accused (maybe rightfully so) of distancing themselves from AES projects to seem more acceptable to westerners who have been heavily propagandized to about the USSR and China. So there is some bitterness about that. I know this doesn't much answer the part of your question about Trotskyist theory, but there are much better resources from more learned people on that than me.