My sympathy is aimed at those advocating anti-racism; BLM isn't the sole preserve of that. You can be an anti-racist and anti-BLM at the same time - I am. Racism exists, it's abhorrent, but in my view there's ways of countering it and BLM isn't it, because it's corrupted and too easy to attack. In football terms, Kick It Out is universally accepted and applauded. BLM was booed. It was because one was political and the other wasn't.
I also don't have to have sympathy with just one set of people. When I say I sympathise with those who boeod, it's because I recognise the situation they were in and the lack of voice they had.
As to why I wouldn't boo? Personal choice. For example, whilst I find defacing statues abhorrent, I do so from a historians perspective, not a nationalist one. I don't feel strongly enough about it to boo, but I have the ability to empathise with other views.
Similarly, do I understand why BLM advocates were offended by the boos? Sure. But on the balance of it, I think it's because they simply don't allow for any nuance - they see it as an attack by racists, end of story. I don't - I see it as an expression of understandable frustration at a cause that has failed by antagonising and patronising at every step.