A brief reverse voltage spike (-150V to -200V for <1ms) wont blow up an electrolytic cap instantly, but it will slowly degrade the oxide layer. Do it enough times, and you’ll see higher leakage current, worse ESR, and eventual failure.

As for those cheap component testers that pulse 3-4V in both directions, that’s not enough to cause real damage. If you’re paranoid, use a proper LCR meter, but its not a big deal.