If your church has no kitchen etc, then how do you share communion together? Do you take everything home to wash?
Did not Jesus share communion with the apostles?
I do not think that God is against a fellowship that can supply nutrition to visitors.
I find it strange indeed.
Communion, also known as the Lord's Supper, contains just two elements. "For I received from the Lord that which I also delivered to you: that the Lord Jesus on the same night in which He was betrayed took bread; and when He had given thanks, He broke it and said, "Take, eat; this is My body which is broken for you; do this in remembrance of Me." In the same manner He also took the cup after supper, saying, "This cup is the new covenant in My blood. This do, as often as you drink it, in remembrance of Me." For as often as you eat this bread and drink this cup, you proclaim the Lord's death till He comes" (I Corinthians 11:23-26).
It isn't a large meal, but a memorial to remember the Lord's death, shared by all members. "The cup of blessing which we bless, is it not the communion of the blood of Christ? The bread which we break, is it not the communion of the body of Christ?" (I Corinthians 10:16). That is what "communion" means. It is a sharing of the memorial meal with Christ and our fellow believers.
It is not a regular meal. Contrary to your "think so" it is specifically forbidden. "What! Do you not have houses to eat and drink in? Or do you despise the church of God and shame those who have nothing? What shall I say to you? Shall I praise you in this? I do not praise you. ... But if anyone is hungry, let him eat at home, lest you come together for judgment. And the rest I will set in order when I come" (I Corinthians 11:22, 34). Regular meals are done at home. The memorial meal of Christ is done in the worship service and the two are not to be mixed.
Fellowship refers to the state brethren are in. We either have a common bond or not. We have fellowship or we do not. "That which we have seen and heard we declare to you, that you also may have fellowship with us; and truly our fellowship is with the Father and with His Son Jesus Christ" (I John 1:3). "And have no fellowship with the unfruitful works of darkness, but rather expose them" (Ephesians 5:11). Fellowship is not a meal. People in fellowship often spend time together and that might include sharing of meals, but the meals are not the fellowship.
In regards to the clean up, the sink in the bathroom has proven to be sufficient to wash the trays each Sunday.
True, when you are not used to following God's plan, it can seem strange to the outsider. "In regard to these, they think it strange that you do not run with them in the same flood of dissipation, speaking evil of you" (I Peter 4:4). But it doesn't imply that these actions are without reason.