If I sell my house and the profit is federal income tax exempt, might I have to still pay local income taxes?

Answer 1

It's possible. Many states, but not all, follow the same rules as federal for profit on selling your house being tax exempt. I don't know of municipalities that charge tax on capital gains, but there might well be some, and they may or may not follow the same rules as federal for exemption from tax.

Answer 2

Without knowing where you are it's not possible to say. Most states do appear to grant a similar exclusion to the Federal one but without knowing where you are it's not possible to look up the answer.