It's unclear what you mean by condoning sin. I'm not OK with throwing gay people out of the Church. Demanding "proper" repentance is not really the Lutheran way, since none of us can be properly repentant. We are justified by faith alone, not faith + proper repentance. At our church, the message is clear: justification is not contingent on regeneration. Our sacraments are effecacious: all who have been baptized into Christ have put on Christ.
On removing a person from fellowship, both Christ and Paul said an unrepentant sinner must be removed. This is not limited to sexual sins. It is quite obvious the sins in question are made public and the party involved is recalcitrant.
Now for sins not repented, the Lord's Table offers the opportunity for each of us to examine ourselves to see if we are worthy to partake of the meal with the church.
In the case of public brazen unrepentant members, should the church offer communion to such members?
I am not familiar with what you mean by "proper repentance." However, repentance is mentioned as the response of those who heard and believed the Gospel.
Jesus required the apostles to teach a Gospel of salvation in His Name and repentance (Luke 24:46-47).
In Acts 2 Peter on the day of Pentecost called all those cut to the heart to repent believe on Jesus and be baptized.
In Acts 3 Peter confirms this message:
Repent ye therefore, and be converted, that your sins may be blotted out, when the times of refreshing shall come from the presence of the Lord. And he shall send Jesus Christ, which before was preached unto you: (Acts 3:19-20).
Paul indicates in 2 Corinthians 7:
For godly sorrow produces repentance leading to salvation, not to be regretted; but the sorrow of the world produces death. (2 Corinthians 7:10)
I don't know how much your Lutheran church has departed from Luther, but Jesus says we must be born from above or what we usually call born again:
Jesus answered and said to him,
“Most assuredly, I say to you, unless one is born again, he cannot see the kingdom of God.”(John 3:3)
Peter emphasizes this as well:
Blessed be the God and Father of our Lord Jesus Christ, who according to His great mercy has caused us to be born again to a living hope through the resurrection of Jesus Christ from the dead, (1 Peter 1:3)
Paul also mentions this to Titus:
He saved us, not on the basis of deeds which we have done in righteousness, but according to His mercy, by the washing of regeneration and renewing by the Holy Spirit, (Titus 3:5).
I can provide more if you like.
It's God's job to save people, not mine. That is consistent with Lutheranism. Loving my neighbor means respecting their autonomy to live their own lives. Dictating how I think they should live would not be consistent with that.
And the NT is all about evangelism. The love expressed by godly people of the NT was to share the Gospel message of Christ crucified, His death and resurrection. That through this ultimate act of Love we can become sons and daughters of God and co-inheritors with Christ.
Jesus told quite a few parables reference seeding and the harvest. Jesus told His disciples
“The harvest is plentiful, but the laborers are few. Therefore pray earnestly to the Lord of the harvest to send out laborers into his harvest.(Luke 10:2)
Paul picks up on this where he says:
How then shall they call on Him in whom they have not believed? And how shall they believe in Him of whom they have not heard? And how shall they hear without a preacher? And how shall they preach unless they are sent? (Romans 10:14-15)
I don't think I indicated that "we" save people. Show me where I said so. God calls and saves people. We are to be His messenger of the Good News.