"I've seen that if either spouse contributes to a Roth IRA, we cannot federal file Married Filing Separately."
There is no such limitation. You are confusing this with a spousal IRA contribution using one spouse's compensation to support the contribution of the other spouse who has lower compensation, which requires filing jointly.
A 403(b) is not an IRA and is not subject to any IRA rules. Only the employee and the employer can contribute to the 403(b). There is no such thing as a spousal contribution to a 403(b) as there can be with IRAs.
