I mostly agree with your post, except on not embracing those who are open about being gay/perverted.
I am from time to time strongly tempted toward adultery. I don't fantasize about women other than my (first and only) wife, and I don't flirt with other women. But opportunities come up - usually to my shocked surprise, since I almost never realize what's coming in those situations. So far, I have as politely but firmly as possible rejected every such opportunity, but I have also been tempted. Very tempted some times. The Church should embrace me - but also frequently, emphatically, and unambiguously reinforce the message that adultery is completely forbidden.
The Church should respond to homosexuality the same. So long as welcoming gays and other perverts includes a frequent and clear emphasis on the relevant scriptures and their proper interpretation (which is that homosexual conduct of all kinds is always wrong), they can be welcomed without harming the Church.
The problem comes when we try to be welcoming by skipping over the parts of God's word that those in need of spiritual guidance don't want to hear. The problem comes when we accept the far left premise that quoting God's word is "hate" and encouraging/celebrating disordered conduct that violates God's word and spreads deadly diseases is "love". A Church cannot accept that premise and still remain Christian.
We are all sinners saved by grace. Christians are called to love sinners, just as Christ did. "While we were yet sinners, Christ died for us" -Romans 5:8.
Just as Christians are anointed by the Holy Spirit to love sinners they are also anointed to hate and shun sin. This doesn't mean Christians are saved by their works or that Christians never sin. It does mean that Christians recognize their sin and repent.
Neither Christians or Christ -- embrace, condone or empower sin!
As far as remarried Catholics and single moms receiving communion? All through my life there's been the hypocrisy of the Church granting annulments very easily to the favored few. Because of that, this issue always seemed a bit bogus.
One reason I have a lot of trouble with the acceptance of those who lead an openly homosexual lifestyle is because of the priest scandal. That hasn't and won't go away. The Church has to clean up its act, and that'll take a few generations.
FWIW, I'm not member of a religion, but am a believer that we have an existence that's spiritual and attached to a greater entity we can't fully know and separate of our physical being. Just don't know that a Church is where my beliefs belong.
Thank you for the excellent discussion.