The NT is unequivocal on the need for baptism:
“Whoever believes and is baptized will be saved, but whoever does not believe will be condemned” (Mark 16:16)
This being said, your question may have a misplaced emphasis. Jesus says “whoever believes and is baptised …” — belief must precede baptism. Those who have expressed a sincere and well-founded belief in Jesus should be encouraged to be baptised as Jesus commanded.
As to how a congregration is organised, this will vary depending on circumstances. The congregration will necessarily engage with many people on different stages in their journey — some just beginning to come to a knowledge of God. It would be inappropriate and counter-productive to suggest that only those who are baptised can interact with a congregation and its services.
On the other hand, some parts of the congregation and its services are special and only have relevance for believers. This is particularly true of the bread and wine. Jesus gave these symbols to his followers to remember him by. They have no relevance to those who have not committed themselves to Christ. Therefore it is usual, and in my view right, that it is expected that only baptised members will take the bread and wine; non-members are asked to refrain.