Here are the rules for the Universal Life Church: 1. Be Kind To Each Other. That's about it. If you want to be Christian, the ULC will accept that. If you want your faith to include Eucharist, the ULC will accept that as well. Remember, when it's your church, you get to make up the rules.
Why would they not be allowed? I think that ordained ministers of this particular church should be able to offer the Eucharist to whoever they feel they believe needs it. I feel like excluding people from the Eucharist is just another way to follow some sort of elitism and keep people out.
Many people, including many main stream ministers, believe that there should first be legal marriage and that then ministers should be asked to bless what has been legally done, as in European nations. So if we are going to let (almost force) ministers to legally marry people, then any arbitrary definition of minister will do.
Yes, ordained ministers of the Universal Life Church should be allowed to offer the Eucharist to Christians, but I don't know of any Christian that would want the Eucharist given to them by a Universalist. The point of Universalism is that there are no rules. So the Universalist can do whatever they want, including giving the Eucharist to Christians. But a Christian probably wants their Eucharist from someone who believes in something.
I don't think ministers of the Universal Life Church should be allowed to offer Eucharist to Christians. The reason is I don't see the Universal Life Church as truly Christian and following the same beliefs. To allow them to do so would be greatly watering down the Christian belief for people.