His criticism is only of people who are giving the impression that the military is aligned with a particular party.
His issue isn't with what they're saying. He even declined to comment on that. This is what he should do, because I don't think senior military figures should criticise the civilian administration in public.
I think you're getting your knickers in a twist over nothing. All he says is it's unhelpful to him, which it probably is!
Re the pride march, it's not partisan political in this way and the US Military has officially endorsed equality of sexual preference so I'd say you're comparing apples and pears.