To "belong" or be "accepted" by religion often involves some kind of conformity or meeting certain expectations. The invitation is often a subtle - “Change and you can follow.” Jesus says, “Follow and you will change” and there’s a huge difference.
Jesus doesn’t expect you to change first - He just makes the invitation to follow Him. Being a sinner doesn’t disqualify anyone from following him nor does being an unbeliever doesn’t disqualify us from following him. Following Jesus doesn’t mean jumping through a religious hoop to make a radical change ourselves all at once.
Following Jesus will almost always involve a sinner/unbeliever taking a small inconvenient step rather than making a radical change. Accepting Jesus invitation means taking a next step.