As with a lot of things immigration-wise, enforcement may have gotten tougher under Trump. However, at least in the past it wouldn't be an issue unless you are charged with a crime for failure to file and/or pay your taxes. If you are charged with such a crime, you would face similar immigration consequences to what would happen if you were charged with any other type of crime. Only a small percentage of people who fail to file actually get charged with a crime, but to eliminate the risk it is certainly good that you are getting caught up on your taxes. I'd say the same thing even if you were a US citizen.
Given that you've been a permanent resident for about 11 years, it sounds like you are in no rush to naturalize. However if you did want to naturalize, the N-400 form asks a couple of questions about taxes: "Do you owe any overdue Federal, state or local taxes?" and "Have you EVER not filed a Federal, state, or local tax return since you became a lawful permanent resident?". Note that it only asks whether you failed to file at all, not whether you filed late. Likewise it only asks if you are currently delinquent on your taxes, not if you were delinquent at some point in the past. So it is probably best to wait to file N-400 (if you want to file it at all) until you are current both with filing requirements and with payment of taxes. At that point you should be OK.