Open Question: In filing MFS, is it mandatory to split incomes or can each spouse just claim their own income?

The spouses live together and pay half of everything (mortgage, property tax, etc). They split these expenses on sch A, but they each report their own income...it that ok? What will the IRS or CA say if they file MFS but each claims their own income and then share the mortgage and property tax expenses? CA is a community property state.