This may be a dumb question, but I'm new to having the happy switch on a personally owned weapon and am a bit confused about the "semi bolts" I've been seeing for both the Shrike and the AR57.

When I look at the FAQ for the AR57, it talks about a DIAS, not a RR. Does that matter, or does the DIAS need the same bolts as an RR?

Also I know the M16-bolt-in-an-AR15-legality debate has been beaten to death and then resurrected to be beaten to death again, but would running a full-auto bolt for a Shrike or AR57 on my SBR present me any issues? I assume not, but I'd rather ask than just assume.

DIAS and a RR function exactly the same as far as the upper is concerned. Having a full auto bolt is perfectly fine for both the Shrike and the AR57. Most production AR15s already come with full auto bolts

And to clarify there is no such thing as a full auto or semi auto bolt in most AR-15 rifle calibers.  The difference is in the bolt carrier.