[NB: the OP seems to have changed using Catholic (in the title, as in Rome) with catholic (in the question, as in orthodoxy). I am answering using catholic (as a noun) with no intended disrespect to Catholics]
The correct sentence of your two examples is
My parents have the same religion. My father, hence my mother, is catholic.
The underlying sentence (main clause) is
My father ... is catholic.
the subordinate clause is
hence my mother (is also)
therefore my mother (is also)
thus my mother (is also)
making the subject of the sentence singular: My father.
Your use of hence is to mean therefore, thus, or so to show causality
Hence is an conjunctive adverb and is usually used to connect the two clauses
My father is catholic hence my mother is also catholic
My father is catholic therefore my mother is also catholic
My father is catholic hence my mother converted
My father is catholic therefore my mother converted
are correct to support the fact both parents have the same religion.
My father and my mother are catholic
My parents are catholic hence my religion.
are also correct.
My father is catholic hence my mother
could mean that because your father is catholic he married your mother (for whatever reason)