There are five main scriptural reasons for closed communion, so a list of the passages would involve all the many passages about these five topics.
The first reason is that communion is fellowship between those who attend, and fellowship must be based on agreement in doctrine. All the fellowship passages would be relevant, for example Romans 16:17. "Keep away from them" cannot mean commune with them. You will find a lot of discussion of this under the topic "fellowship" on this site and in the book Church Fellowship: Working Together for the Truth."
The other four reasons are touched on in 1 Corinthians 10 and 1 Corinthians 11.
Communion is based on faith in Christ, so non-Christians cannot attend.
Communion is for forgiveness so the impenitent who are living in a sin cannot attend.
Communion calls for self-examination so the uninstructed cannot attend, even our own children.
If communicants do not recognize the presence of Christ's body and blood in the sacrament, they receive it not to their blessing but to their condemnation, so members of churches that do not believe in the real presence cannot attend with us.
Closed communion is not a doctrine particular to WELS. Historically, it was the practice of virtually the whole Christian church until quite recently. It is still the practice of the majority of the world's Christians--Catholic and Orthodox. It is the official view also of the Missouri Synod.