I don’t think this is correct.

I’m a middle aged man in poor overall shape but I can still do cartwheels.

I’ve never been able to do a pull up.

Cartwheels don’t require much strength. You aren’t on your arms for very long and don’t actually further extend your arms during the period when they’re touching the ground.

What cartwheels do require is coordination, flexibility, and balance.

… and practice. Lots of practice.

If I had to guess for most people the limiting factor as you age would probably be flexibility.

That’s assuming you knew how to do them when you were young. I learned it in my mid twenties, but would not envy someone trying to learn it in their mid forties or later.