Different churches has different policies for who is allowed to commune. They all have statements about why certain people are allowed at the table and while others aren't. But why should anyone be left out?
If Communion is the "foretaste of the feast to come" then everyone should be invited. Like the parable says invite everyone you see and go out to the streets and bring them in. It is a meal of Grace, undeserved. If Jesus is the host, then why are we putting regulations on it. Aren't we attempting to undo what Jesus was trying to do? Jesus came and shared meals with everyone.
It seems more natural to invite someone to a meal then to have then go through an initiation process (baptism) before they are allowed to eat. This makes communion a meal for insiders.
I've been baptized, and I'm a Christian, but if you want to evaluate my current level of faith before communion there are days I wouldn't be allowed. As I sit in the pew, I'm not sure what I believe or if the word Christian would accurate describe me, but I always take communion because I believe God is bigger than my doubts and the my neighbor has faith for me when mine is lacking.
So, when someone new walks into a church and feels compelled to participate in communion, even if they don't completely understand what it is about, I do not want them to be turned away. God is working in them, and we shouldn't let anything, our rules, misgivings, or tradition, get in the way.
Afterall, Christ is the host of the meal and is present, so let him decided who can come and eat. As far as I can tell, Jesus ate with lots of people and you didn't have to jump through any hoops to be invited.