Membership in the Knights of Columbus is open to men 18 years of age or older who are practical (that is, practicing) Catholics in union with the Holy See.
A practical Catholic accepts the teaching authority of the Catholic Church on matters of faith and morals, aspires to live in accord with the precepts of the Catholic Church, and is in good standing in the Catholic Church (source).
If a Catholic man had just cause to seek or to accept a civil divorce as a means of legal separation from his wife, and is currently living a life of chastity appropriate to a married man, he would presumably be in good standing in the Church. If he subsequently was granted an annulment and later remarried according to Catholic marital law, those circumstances would not affect his standing in the Church. He would then meet the qualification of “good standing in the Catholic Church” required of a Knight.
On the other hand, if a Catholic man divorced his wife without just cause, is involved in an extramarital romantic relationship, and/or has remarried civilly without an annulment from the Church, then he is not considered “in good standing in the Catholic Church.” You would have to confirm their policy with your local council of Knights to be certain of this, but it would seem to me that these circumstances would disqualify such a man from membership in the Knights.
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