Regeneration has nothing to do with belonging to a religious group, or not belonging to a religious group. Regeneration is a work of the Holy Spirit in a life. Jesus referred to it as becoming born again. It is the work of the Holy Spirit making a person a new creature in Christ. The Holy Spirit has made all things new in a life when He has regenerated that person. I'd give you the verses, but I know you don't believe in the Bible.
Now if you are talking about a person renewing their mind after they have become regenerated (saved), that is a different story. God has instructed us to renew our minds. Again, I'd give you the verse, but again I know how you feel about the Bible. A religious group can definitely matter in that case. If we hook up with the wrong group we could learn a bunch of false doctrines. Our minds would not be renewed at all, but instead be brainwashed with false teaching. Sometimes smaller groups are more accurate than larger ones, but not always.