(1) Adultery is not your average indiscretion. Breaking a marriage contract is illegal in most jurisdictions (though it is rarely enforced).

(2) When you teach at a religious institution, "personal life choices that don't affect their work?" is less of a thing, because you've deliberately related work and religion (i.e. personal choices).

It might not be your cup of tea, but some students want to attend an institution of high moral standards, as well as high academic standards.

>high moral standards, as well as high academic standards

I don't find cheating to be especially immoral, at least not more than lying or withholding information for any other purpose.

You can bring up D'Souza's getting fired for cheating on his wife with the Board of Trustees of King's College. Their address is:

  56 Broadway, New York, NY 10004

Since King's College is an accredited, Christian liberal arts college, I can only assume that they demand the highest moral character from their professors and administration. And stuff.

Why would I? I don't care about their views on morality, and they can decide whatever they like. I wouldn't regard religious schools as a quality education though.

But I'm not sure why extramarital relations are being brought up as a way to discredit someone, when it's of zero relevance.

It's a Catholic college.