No, this isn't true. Rittenhouse went to Kenosha because of a Facebook post asking for armed citizens to defend businesses from rioters and looters. This looting had been happening for two days largely unopposed by police.
I don't believe the people doing that looting cared about BLM at all. And I don't think the militia went there to stop them because they opposed BLM. Rosenbaum, the first man to be shot and arguably the person who instigated the events was confirmed not to be there in support of BLM. I don't think the issue was racism or peaceful protesting but rather looting.
I think we agree that Rittenhouse shouldn't have been legally entitled to carry a gun, and that it would have been much better if the militia hadn't been there. But I don't understand the argument that because Rittenhouse didn't personally own the property, he should have ignored the fact that it was being destroyed. Should we really take the attitude that we shouldn't act unless a situation directly impacts us? By that logic, nobody should have been protesting Jacob Blake's shooting. Certainly nobody white. If I owned a business in Kenosha and looters were destroying it with little to no response from the police, I think I'd have been grateful for any help I got.
I don't think anybody in the militia went there with the intention of killing anybody or was weighing the value of human life against the value of property. This is supported by the fact the only people other than Rittenhouse who fired a shot that night, were people who weren't members of the militia.
Again, to be clear, I don't think that they were there to support black lives either. I'm just saying that the situation on the ground wasn't as simple as "racists vs BLM".