I've never heard of a car or any other RFID fob causing interference with a credit card, but I guess it's possible. You might have a damaged card, or the merchant didn't enable the tap feature. I do notice that smaller merchants like restaurants or convenience stores don't always have tap to pay. It's likely because the bank charges them extra for that "feature." Big chains can afford those extra charges, but that doesn't stop the machines from not working.
Most banks now have mobile payment aka Tap to Pay built into their phone apps. Naturally, it only works with bank credit cards though. You register your card in the app and then you can use your phone to tap on POS machines. You do need a smartphone that has NFC built-into it to be able to use tap to pay. Most phones should have NFC built-in these days, but make sure to check.
There's also Apple Pay and Google Pay that do the same thing as the bank apps, but with just about any credit that has a Tap to Pay icon that looks like a WIFI icon.