I think that opting out of a component of the group identity doesn't necessarily lead to alienation.

This is true, but a ritual designed explicitly as a group-bonding exercise (and, it seems, the most prominent such exercise) is more likely to be something opting out of which contributes to alienation than, say, caring about FAI.

Do you mean signaling that you're not part of the group, or feeling that you're not part of the group, or both?

Both. Although I didn't so much mean "signaling that you're not part of the group" as "doing something which is interpreted by other group members as an indication that you're not part of the group", but the difference is of emphasis at best.