At the time of baptism, one or both of the parents had a credible profession of faith; however over time, it became obvious they did not.
I see in an earlier thread that the term, 'credible profession' is in disregard; but how else are we to examine someone. I don't think you are, but are you saying baptized everyone (supposedly believer and infant) without any examination; then let them be a covenant breaker if that becomes the case.
1. Question: What is a credible profession of faith? Depending upon what the examination entails, e.g., what questions are asked one could conclude that the applicant is qualified to be taken into membership when in fact they are not. Can we as mortals have an infallible knowledge of who is actually regenerate and who is not?
But obviously, Christ gave the responsibility to Elders to have reasonable wisdom to make such a determination. Again, what the criteria is used will determine the result; bad, wrong or missing questions concerning doctrine and life will most always result in a wrong conclusion.
2. I am going to assume
that the second part of your reply is not addressed to me personally because I would never, nor have I ever suggested that anyone applying to membership should not be examined by Elders. My position is akin to what Jonathan Edwards wrote about at length concerning membership in the church which doubtless the majority of people in our day would reject without hesitation.