Double standard, special pleading or false equivalence and faulty comparison fallacy or all the above?

It is fine to compare things - even if they seem quite different. In fact, this is the point of a comparison, to tease out similarities and differences. People often try to argue otherwise (e.g. "there's no moral equivalence between X and Y!", a phrase which is missing the point). This helps in forming moral judgements - if we take A and B, and treat them very differently, a closer comparison could reveal that they're quite alike - and we were wrong to believe otherwise.

However, sometimes the common standard by which they're being compared doesn't make sense - this is the faulty comparison fallacy (e.g. "broccoli has less fat than the market leading candy bar" - in this case, whether it's true or not doesn't really matter, since chocolate is a treat that doesn't exactly advertise itself as low fat in the first place).

In this case, it is fine to compare 9/11 with 1/6 - they were both major civil disturbances that affected the U.S., with important political repercussions. What matters is where you are going with it. Note that 9/11 was responsible for far more deaths, far more property damage, (arguably) spread more fear across the country, and was thus the worse tragedy - which would imply treating it more seriously than 1/6 (otherwise, you'd get a false equivalence). That said, the fact that one thing is worse than another doesn't mean that the original thing is acceptable - if a Trump supporter reasoned like that, this would be a relative privation argument.