Normally, the engine itself uses proprietary signaling for its systems internally, but will present a standardized interface to the avionics.
Granted, plenty of de facto standards exist long before they're codified into a formal document. So maybe the Blackbird actually does use it, or something close enough for a dinky little converter box to do the job.
According to that Wikipedia page, out of the first 6 jets to officially use MIL-STD-1553, only one of them was a Lockheed product. That single Lockheed product was the P-3C, which was a retrofitted version of a plane Lockheed started making more than a decade earlier. To me, that suggests that, even if MIL-STD-1553 existed as a de facto standard at the time of the SR-71's contstruction, Lockheed probably wasn't using it yet.
All speculation, obviously. But the timeline leaves me with doubts.
There's still part of me that can't quite believe that the SR-71 wouldn't be an exception. You don't just make a turbojet out of 1965 technology, without something being so wackadoodle batshit crazy as to make comparions to all other planes pointless. Another commenter mentioned something about a "hydraulic computer?"
I'd love to be wrong. It'd be hilarious if some madmen from the 1960s built a Mach 3 jet out of mostly-normal parts, and then that mostly-normal jet turned into American patriotic folklore. And yeah, I'd feel a bit of patriotic euphoria to see a Blackbird in the sky! I'm not above that.