Hi there!
Baptismal regeneration is one of those theological terms that the majority of people who believe it don't even know they believe it!
Officially, the UMC does not teach or affirm Baptismal Regeneration. That is to say, you will not find those terms (at least, I don't believe so) in any of our official teachings (Book of Discipline, Book of Resolutions, etc.) If you look up "baptismal regeneration", the variety of sources you find will not list United Methodists as a church that affirms or teaches Baptismal Regeneration.
That said; at it's very core- Baptismal Regeneration is a belief (And I am ruthlessly simplifying here, from my understanding, as I am a bit theologically weak on the subject of Baptismal Regeneration, so bear with me) that while Baptism is not an absolute requirement for salvation for everybody, it is crucially important. It changes us, it effects us tremendously, and it is a necessary aspect of any follower of Jesus Christ and should not be considered 'optional'. So while it isn't a requirement for salvation, it's darn close. And as God judges us individually on our hearts, and salvation is not a "must be completed" checklist; it's perhaps even possible that for some, baptism is in fact a necessary means of Grace for their salvation as it's what God has called and commanded them to do.
If that's the core belief of Baptismal Regeneration, then that's something that you'll find the United Methodist Church to be in agreement with.
To continue; our theology on Baptism is that it is a sacrament, and that it is not a repeatable sacrament. That means you are baptized one time. We affirm all Christian baptisms, all methods of baptism, and baptism at every age (though we typically baptize infants, and typically through sprinkling and pouring, but I'll get to that in a moment). That means that whatever Christian tradition you are from, if it was a valid baptism that invoked the Holy Spirit and called upon Christ for your transformation into Christ's holy church, then the United Methodist Church will not re-baptize you. If you feel the need, the UMC has services to help you re-affirm your baptism. But as we believe Baptism is a direct act of God, and as we believe it is the non-repeatable sacrament, we will not re-baptize you.
We baptize infants and later confirm them as youth. This is along the same theological lines of one baptism; it's a lifelong journey. We "remember our baptism" and begin to be responsible for the call our church family and our family put on us when we were baptized as small children. There are many ways we do this; one of which- is communion!
While baptism is the non-repeatable grace, communion is the repeat-as-often-as-you-can Grace. Communion is where we re-affirm our faith. Communion replaces any need for re-baptism, as it has tremendous power in a baptized believer. We affirm that communion is a sacrament, and in our understanding; a sacrament is an outward sign of an inward grace. Communion is the sacrament we receive as often as we can. We also believe that Jesus Christ sets the table and invites to the table through the Holy Spirit. That means that we do not believe we have the authority to say no to anyone who wishes to come to the table. You could say that "we have open communion", but I don't like that term. The reason being? United Methodists don't have open communion; they simply set the table for Christ; who is the ownership and officiant of that Communion. And we believe he will be the one to invite you to the table, and doesn't need us getting in the way of that. While an Ordained or Licensed member of the clergy must officiate, it is ultimately a table of Christ, not any Clergy, nor any Church nor conference nor denomination.
Methodists also take a theological stance somewhere in the middle of Consubstantiation and Transubstantiation. We don't believe that the bread and juice become, on the table, a literal body and blood of Jesus Christ. That is to say, once the elements are consecrated, they are still bread, and still juice. But at the same time, they are holy consecrated elements. They are, in fact, a means in which we partake in the Body and Blood of Christ. One way you might consider it, is that the consecration of the elements is only half of the equation, not all of it. It becomes the body and blood of Christ for you when it is received by you. It is so much more than a symbol in our understanding, but it also wouldn't be correct to call it transubstantiation, as some churches believe.
Does that answer your question? I'll second the above posters comment to read "This Holy Mystery". Know that if you attend a United Methodist Church, you are free to take communion. That's not a church-by-church thing, that's a set-in-stone law of the church. You are invited. Period. Reading "This Holy Mystery" will help you to understand what it is you are invited to, and is much more in depth than my little snippet I wrote.
I would love to clarify if you have additional questions. Please let us know!
As an add, in some traditions, it is considered immoral, sinful, or a conflict of conscious to take communion in a church that serves it openly, or to take communion in a church that is not their own (for example, Roman Catholics would consider a catholic taking communion in a UM Church sinful). If that is the case with you, or for any other reason of conscious you feel you shouldn't receive, I would encourage you to approach the table with your arms folded across your chest. These instructions are a part of our communion liturgy but are sometimes omitted by clergy out of habit (in churches that don't routinely see a lot of ecumenical visitors). Coming to the table with arms folded is a sign that you don't wish to partake in communion, but that you would like a prayer of blessing to help you participate in the means of Grace we share. I would encourage anyone who attends a United Methodist worship service where communion is served, but feels they can not or should not partake, to come forward for a blessing.
