Are Mets fans generally Jets and Isles fans?

I’ve always been curious to know if Mets and Yankees fans are consistent with their football and hockey teams too.

As a non New Yorker I have in my head that it’s

Mets, Jets, Isles (not sure about basketball) Yankees, Giants, Rangers

I’m not sure why I have these teams associated together. I know I’m probably wrong, but just wanted to hear from Mets fans and get an idea how teams a chosen when you have so many to choose from.

Thank you for any insight you can provide!