I feel as if certain churches are not as welcoming as others, but...?

If Jesus teaches Christians to open their arms to newcomers in the faith, why are there such strict rules to communion etc.? Why can't those partake in it that haven't gone through certain rituals? It makes the whole things seem very clique-ish and casts away outsiders. I have found this to be true with the Lutheran denomination and the Catholic faith when I tried to take communion although I was never initiated into the faith. Does God demand such initiation as a college fraternity does? Doesn't he just see that our hearts are right and love hime? Isn't it a paradox to welcome new people into the churhc, but say they aren't "truly" a part of the church and can't take communion if they havent' been initiated? It just seems a bit hypocritical, but I could be wrong. I just felt weird staying behind in my pew at m during communion. I felt like I should partake even though I knew I was not yet a member of the Catholic church. How should I have reacted instead?