I'm considering getting aftermarket sights for my M&P®9 M2.0™ 4" COMPACT. Do I have to buy sights made specifically for the M&P, or is the cut in the slide "compatible" with some common standard? (I know just enough to know that I need to ask the question.) Thanks for the help!

If you buy sights from the most popular companies like Ameriglo, Tru-Glo, Trijicon and Meprolight, they will have models specific to the M&P line.

Look at their websites and they'll show ones that are guaranteed to fit the M&P's.
Getting your old factory sights out can be a chore though, they are in tight.

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U. S. Army Veteran

Most sight makers have specific sights for specific guns. I like Ameriglo "Hackathorns," but YMMV.

Agreed with above.
Simple answer to your question:
"Do I have to buy sights made specifically for the M&P[...]"
is YES. Buy sights for M&P (1 " slide length difference doesn't matter, you are fine between 4" - 5")

I replaced my M&P9 M2.0 5" stock sights with Dawson Precision Charger Fiber Optic sights. Smith & Wesson Sights

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O L James III
CPT Army Ret FA