The examples are too numerous to respond to right now, this late, but, no, there are no illegal marriages, but there may be some wrong ones. Either way, while a marriage may be dissolved, there remains the fact that a marriage occured previously, whether moral or otherwise (You mentioned incestuous types). Marriage is Marriage, and a Marriage is never not a marriage, just a past marriage.
There is no prevention against divorcees becoming members of a local assembly, but there is a condemnation by Jesus that those who marry divorcees are living in a state of adultery, so the Local church should consider this, and probably decide against for mal membership because Jesus Himself calls this sin. That does not mean the couple cannot attend worship, nor does it mean their children are condemned y God or something, just that they are in sin. God can still bless them but never the way He would have if there were no previous marriages.
With the commanality of divorce today, if all divorcees were prevented from worship, 1/4 to half the church populations would disappear, regardless of what denomination.