Should there be an open door at church to sinners un-repentant of their sins?

NO! here is what Paul says on matters of conducting a church assembly.

1 Corinthians 5

1It is actually reported that there is sexual immorality among you, and of a kind that is not tolerated even among pagans, for a man has his father’s wife. 2And you are arrogant! Ought you not rather to mourn? Let him who has done this be removed from among you. (the church and fellowship)

3For though absent in body, I am present in spirit; and as if present, I have already pronounced judgment on the one who did such a thing. 4When you are assembled in the name of the Lord Jesus and my spirit is present, with the power of our Lord Jesus, 5you are to ((((deliver this man to Satan for the ((((destruction of the flesh)))) (death sentence -Leviticus 20), so that his spirit may be saved in the day of the Lord.  Extreme isn’t it? Is Paul a bigot or excising justice to the community?

Of Couse I am only using this reference to carry the point of expulsion from the church. (No open door).

Paul now elaborates to include all sexual sins and other fleshly un-repented behaviour.
   9I wrote to you in my letter not to associate with sexually immoral people— 10not at all meaning the sexually immoral of this world, or the greedy and swindlers, or idolaters, since then you would need to go out of the world. 11But now I am writing to you not to associate with anyone who bears the name of brother if he is guilty of sexual immorality or greed, or is an idolater, reviler, drunkard, or swindler—not even to eat with such a one.

Paul ends with a clear explanation on when to apply righteous judgment for those in the house of God “the church” to outsiders who live in sin.

12For what have I to do with judging outsiders? Is it not those inside the church whom you are to judge? 13God judges those outside. “Purge the evil person from among you.”

 

Homosexuals, paedophilia, bi sexual, fornicators, transgender and bestiality that are known for actively living this lifestyles can step foot into a church but cannot be accepted to stay is un-repented. We are not to even eat with them (who proclaim to be saved). The passage does not say that we cannot associate with them as un believers.

Can a Christian show the love of Jesus to a sinner or homosexual?

YES! Witness the fruit of the spirit to them as Jesus would.  

Matthew 5
 43“You have heard that it was said, ‘You shall love your neighbor and hate your enemy.’ 44But I say to you, Love your enemies and pray for those who persecute you, 45so that you may be sons of your Father who is in heaven. For he makes his sun rise on the evil and on the good, and sends rain on the just and on the unjust. 46For if you love those who love you, what reward do you have? Do not even the tax collectors do the same? 47And if you greet only your brothers, what more are you doing than others? Do not even the Gentiles do the same? 48You therefore must be perfect, as your heavenly Father is perfect.

The church with an open door and having the status of “we welcome all” to Christ inside this building is a misuse and twisting of 2 very important issues.