I did apply for state and SSDI at the same time - state was just approved faster.

Once SSDI was approved, my state continued for a few months, and then I asked them to discontinue the benefits because I was about to get married and I did not need the state anymore once I was married (Plus once I got married I would not qualify for state anymore anyway).

I never meant to imply that you can't do both together. A lot of people get both state and SSDI and have state Medicaid and federal Medicare at the same time.