If the group has less than 25 members, it can do whatever it wants. Once it gets above that level, it must not discriminate against people on the basis of a protected characteristic.
Your darts ability is not a protected characteristic, so the pub darts team can exclude you on that basis. Indeed, if they have fewer than 25 people they can exclude you on any grounds they want. However, if they have 25 or more people in the team, they could exclude you for being shit at darts but not for being a woman.
Yes, a lesbian group could say "we are full" to any trans woman who applies, but if they have more than 25 members and the individual concerned discovers that they have admitted women after rejecting them and without anyone leaving, they have a case for discrimination.