We were listening to a very good teaching last night on the subject of families, and the preacher made a point that I think applies in many areas of our Christian walk. He said that Jesus always preached the ideal - what God expects, what is holy and right - but He always dealt with people in their reality - where they were at that time. In other words, there is a holy standard that Jesus wants us to strive for, that we are to live our lives to try to achieve. But His Grace meets us where we are right now, forgives us of our sins and gives us the strength to continue to strive for that ideal - even though we will never reach it in this life or in our own strength. But we are never to use the fact that we cannot achieve that ideal as an excuse for not trying to reach that goal.
I cannot imagine Jesus ever saying that because of a mistake in your past for which you have repented, you can never fully participate as a member of the Body of Christ.
The problem is that Church simply does not recognize the second "marriage" since in its eyes, it does not exist. There is one and only one marriage and what God has joined, man cannot rupture. This does not mean that those in irregular unions are "forever lost". True repentance in this case would require heroic chastity and abstinence from sexual relations with the current partner. Examples of this are likely rare but not unknown.
Forgiveness of sins means that we don't continue to live in a state of sin. That's the issue here. However much the breakup of a marriage is regreted, subsequent unions, in which sexual relations occur outside of marriage, are objectively sinful.
While I am not a Catholic either, I think their response to your point is Jesus' statment that someone who is divorced and remarried is in a continuing state of adultery, thus it is hard to claim repentence when one is in continuous adultery.
Your comment: “I cannot imagine Jesus ever saying that because of a mistake in your past for which you have repented, you can never fully participate as a member of the Body of Christ. “
Jesus cannot embrace sin. He can and does forgive sin with the understanding that the person will go and sin no more. Jesus can not condone someone to continue to sin by having relations outside of marriage. Jesus is a just judge, but also has divine mercy.
The repentance that is needed is for the ongoing adultery that violates a still existing marriage. Repent from that and start living a chaste life that respects that you are still married to your first spouse and you can receive Communion.
What is your definition of "repentance"? According to your definition, if a person continues to commit a sin, has he "repented" of that sin?