Most homeowners have fixed rates. A rise in interest rate will only make the house underwater in value and not affect their monthly payments
If fed rates ever go back to 5%, which they haven't been since the 90's, then mortgage rates would go to 7 or 8 percent.
it's the monthly payments not the price of the house, and if rates go up because the Fed has to chase inflation, then those monthly payments go up, and affordability goes down.
If people's income have been increasing,they will be able to afford slightly higher monthly payments but it's all going to be eaten by interest.