Do capacitors have a polarity?

I know that this is a dumb question, but here goes. Basically, my central AC system from the early 2000s has been having a hard time starting up. It used to come on almost instantly, but it recently started struggling to start and browning out the lights for about 1 second when it starts up. However, once the system is running, it runs great. I checked the cap, and it was very corroded. I installed a new capacitor, and the unit starts up instantly again. The cap for the indoor blower motor seems weak too, so I went back to that HVAC shop to get a new cap for that too, and the guy warned me that they have a polarity, and the cap may work fine if connected backwards for a little while, but it can explode and start a fire with no warning. That doesn’t sound right to me, but I’m far from an expert. I thought that AC caps don’t have a polarity since the current alternates anyway, hence the name “AC”. Could someone please verify that the capacitors don’t have a polarity? Thanks, I just want to make sure that I didn’t screw up.

Capacitors used in electronic have polarity.
The capacitors we use in AC&R do not have polarity.

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Originally Posted by chemi-cool

Capacitors used in electronic have polarity.
The capacitors we use in AC&R do not have polarity.

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My understanding is that AC capacitors don’t have a polarity since AC alternates, but DC capacitors have a positive and negative. Is that correct?

That's what he said, electronics are DC.

The HVAC shop guy is either lying to you or is incompetent.

Only ever witnessed one explode wow how do they get all that stuff in a small tube