Let me give you my two cents worth.
The issue on "unequally yolked" sometimes is overly
and wrongly quoted. Strictly speaking, just from that verse, a
Christian should not even enter into a business partnership with a
non-Christian.
Difference in doctrine? it depends on how much
"doctrine" exchange of ideas within the marriage. If the couple can
agree to disagree, why not?
I have two sets of close friends who are in this
arrangement. No problem. One set of these friends actually worship
in my church, Catholic wife in a Protestant church, no secret, no
issue.
Such an arrangement only matters if:
one partner sees the other's faith as heresy. In the
first place, the marriage may not have occured.
people around this couple encourages the couple
concern to "convert" each other to the "right" doctrine.
Such an arrangement would not matter if:
the couple concern are happy with the status.
the couple concern does not see any major
differences between RCs and Protestants.
the couple concern doesn't what anyone else feels, a
marriage is between them and God, and if God is not happy with
them, God will deal with them in His own time.