When filing your Stimulus Registration you only have three choices, Single, Married, or Head of Household.  If you are Married Filing Separate, you would need to select Single to proceed through the registration.  

I’m in the same boat. I am not required to file a tax return. When I try to complete the stimulus only return, it won’t let me file as married filing separately and rejects me if I put single as TurboTax directed me to do since my spouse already filed married filing separately.  

https://www.irs.gov/coronavirus/economic-impact-payments

Have you tried the one on the IRS website?