We’ll be staying in Getaria in early September. We will be flying back to Madrid and then New York from either Bilbao or San Sebastián. From what I can tell, the airports are equidistant from Getaria. Both flights to Madrid are in the early morning. My question: Is one of these airports preferable?

Bilbao is a larger airport serving both international and domestic flights. San Sebastián airport is actually in Hondarribia, along the river across from France and only has domestic flights. We found the flights were more expensive, fewer choices in SS, but more convenient to SS.

In your case, any will do, price should be the decision factor.

Go from San Sebastián. Airport.As The closest airport to Getaria, Spain is San Sebastián Airport (EAS)

You cannot do that with a direct flight.
Will that not depend on your requirements. What are they?

Bilbao airport appears to be almost twice the distance from Getaria. Although the flight from Bilbao to Madrid is far less expensive, the longer drive to Bilbao seems to suggest that San Sebastian is the better choice for our flight to Madrid, en route to New York.

According to Google Maps it’s only 15-20 minutes quicker to go to San Seb Hondaribia airport. If you are returning a rental car have you considered the rental company you will use and if they have a return at San Seb airport?

I drive on that route around 50 times a year. Flying to Bilbao will certainly be cheaper and the drive will be just 15 min longer. Also, there´ll be more car hire options in Bilbao than in the tiny airport of San Sebastian. And connection to the highway is faster from Bilbao airport. There may be a minimum difference in the toll charge (around 3 eur difference). In any case, as said before, differences are not relevant, choose the airport based on what you think is relevant (landing times, price,...)

Is MAD just a layover airport on the way to New York?
It seems you are looking at the driving time to the starting airport as the determining factor. This is probably a 30 minutes difference at the beginning of the trip.
Other consideration might be:
Layover logistics consideration. Is there enough time at the layover airport?
Foul up recovery. If your flight out of either starting airport get seriously delayed, what fall back options are available? Even if the liability falls on the carrier, they cannot offer non existent options. There are significantly more ways to get out of BIO to get back to New York than from San Sebastian.
Are the available seats for both options acceptable to you?