If a married couple owns a rental property (A) in one state and owns another house (B) in another state (the latter of which serves as primary residence during the marriage) and then decides to separate, can one party move into the rental property A and convert it to his/her primary residence for the purpose of filing taxes even though they are still married? The other spouse would continue to use property B as their own primary residence for tax purposes. This would assume a 'married filing separately' scenario.
Or can there only be one primary residence for both parties even though they are separated, they live apart, and they file separately?
You can each claim a separate residence. However, your allowed deductions will be cut in half when filing MFS. For example, MFJ can claim a maximum of $10K in State and Local Taxes (SALT). But when you both file MFS, you can each deduct only $5K of SALT.
Check your state laws but you can only have one primary resident for the HOMESTEAD exemption on your RE taxes but for income taxes you can either file a joint return or a separate return using different addresses. The Sch A deductions on homes allows you to claim one primary home (homesteaded) and a second home for mortgage interest (limits apply) but all of the RE taxes limited to the SALT limitation. Before you file separately you both need to discuss this because if one spouse itemized deductions then the other must also itemize even if that amount is less than the standard deduction.