Will our unpaid taxes affect us when we apply to remove the condition from my husband's green card?

No, not likely, as a matter of examiner discretion. You were obligated to show that you could support him at the time of filing. You remain financially responsible for him, whether you are married or divorced, for ten year or until he becomes a naturalized U.S. Citizen. If he has a catastrophic medical issue, then the medical care provider or U.S. Government may seek reimbursement from an I-864 sponsor.

You will need to provide more evidence to demonstrate the ongoing marital relationship, where he is filing a joint petition with you. Neither the evidence that needs to provided for the form I-751, nor the form in which it should be submitted is very clear. Hopefully, this will not pose any other challenges in the process.

You may want to schedule an appointment or teleconference with an experienced immigration attorney to provide assistance.

The above is general information not meant to be legal advice. The above reply does not create an attorney-client relationship.