That might be a Double standard or Hypocrisy.
A double standard is the application of different sets of principles for situations that are, in principle, the same.
Hypocrisy is the practice of engaging in the same behavior or activity for which one criticizes another or the practice of claiming to have moral standards or beliefs to which one's own behavior does not conform.
Also the point about fallacies is to find out that something is wrong with an argument and narrow down where the problem in the reasoning lies. It's not to give the fallacy a fancy name...
Like the problem with the "No true Scotsman"-fallacy is that you retroactively change the definition.
Like if you have a definition: "All true Scotsman are born and raised in Scotland", then Brian from Ohio who had Scottish great-grandparents is not a true Scotsman. However if you'd argue that Andrew from Aberdeen is not a true Scotsman because he doesn't eat haggis. Then this is in so far fallacious his eating habits have no barring on his Scottishness as far as the definition is concerned.
So to avoid that being a fallacy you'd had to have stated beforehand (and found agreement) what constitutes a true Scotsman.
Also the nature of the group might matter quite significantly as to whether it is or isn't a double standard or a hypocrisy. Like did the membership comes before the purpose of the group, idk friends or family where the bond comes before any explicit purpose of the group. Or are you talking about a club, where the purpose of the group is laid out before there are any members or is it an informal group like "bearded people" where obviously a bearded guy who shaves clean is no longer a bearded guy. Likewise if your club makes it their raison d'être to not act reprehensible then you've more of a claim to expel them on the basis of that then if they are just part of a group of friends where that is not a necessary condition for membership.