(having given this a bit of thought):

Some people feel that the truth value should reasonably be changed under reversal. I think this might be because humans expect a social convention where info is given in order of relevance. So if (a) comes first, this is info that maybe the parade is crowded-by-default (e.g. preemption is the norm). This makes (b) implausible. If (b) comes first, this is info that we should expect to see people, by default. But this can still be preempted by an exceptional situation.

I don't think this is even about counterfactuals, specifically, but about lack of commutativity of human utterances (most logics and mathematical languages allow you to commute propositions safely). I can think of all sorts of non-counterfactual versions of this where expectation-of-a-default/preemption create non-commutativity.

There exist cases where people gave "Pearlian accounts" for these types of things (see e.g. Halpern and Pearl's paper on actual cause). But I think it requires quite a bit more work to make it go through than just "surgeries and causal graphs." Their paper is quite long and involved.