Yes, you can apply for U.S. citizenship with unpaid taxes, but it can affect your application. USCIS will look at your tax history when evaluating your 'good moral character' to decide if they should give you citizenship

It can affect your application for citizenship and it may not. Its best to pay all your taxes before you apply.

Yes, you can still apply for U.S. citizenship even if you got unpaid taxes, but it might mess with your application. You need to show you got a plan to pay back the IRS, 'cause having unpaid taxes can make them think you don’t have "good moral character," which you need for citizenship.