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Should professing Christians who marry unbelievers be regarded as unbelievers themselves (until they acknowledge & repent of their sin)?

That is a tough one, seeing how the professing Christian isn't subject to a local Church. However, unless I misunderstand the applicable Scripture passages the same principle can apply in this case.
However, before I went as far as considering them as unbelievers, I would make absolutely sure that the person knows the motives for doing so. That would mean pointing them to the applicable Scripture passages before doing so.

Just a word of warning, if you follow through with this, you may take some flack and in the eyes of some.

I am in a similar situation with my sister in law. She is a professing Christian, who has been dating a non-Christian for a few years now. Taking month long holidays with him and living part time with him at his house.
It is even more complicated than that, she is an extremely unforgiving person, who is easily hurt. She is slowly losing the respect of her family, because of this and is acting like a bitter old woman.
She also is working towards a degree in Christian counseling, so you can guess what the family thinks about that.
To make a long story shorter, under the counsel of my pastor I wrote her about the concerns I had about her.
She has completely denied all the accusations I made against her in the letter. She also told me that she will never talk to me again until I apologize. She also says she is concerned about me because she believes I am getting unbiblical counsel from the Church I attend. In other words she believes my wife and I are attending an unbiblical Church.

I mention all this, just to say that when we step out and try to do what we believe Scripture says on a given matter, it may not be well received. However, we answer to God, not others. Doing the right thing is not always the easy thing.

Tom