Does the military spouses residency relief act still apply if the military spouse is filing separately?

Yes, It applies to Married filing Separate returns and Married filing Jointly returns, but not to Single or Head of Household statuses.  MSRRA rules are no longer applicable if:

• The service member leaves the service.
• The couple divorces.  Once you are legally separated or divorced, MSRRA no longer applies.  
• The service member moves to a new location where the spouse could join them but chooses not to.  If the deployment is to a location where the spouse is not allowed to follow, it does not affect their MSRRA eligibility.
• The spouse clearly establishes the new state as a state of residence. This includes an action like applying to vote in that state.

Military Filing Information on State Websites