Well, Esther, I'll agree that how it is handled after the fact is kinda rude, talking about who was invited and who had the audacity to show up uninvited. But I also think showing up uninvited is rather rude as well.
But addressing the party issue itself, that she's having the party at her home and she's inviting a bunch of club members, I don't particularly think that, in itself, is rude. Perhaps the mention of "club" was not to make it an official club party, but just a way of saying that she's inviting a slew of club memebers so they'll all know who will be there. We probably need more detailed info. I mean, if the club is ten people and two don't get invited, then yeah, that's rude. But if the club is 60 people and 20 don't get invited, that's more understandable...40 people at a party (in your home, no less) is quite a bit!
So the only alternative is to not have a party at all, unless she doesn't invite anyone from the club, or even mention the club. Because, even if she invites a few club members it will get around that she did so, and she will be in the same boat. I personally think people need to stop trying to read so much into it and understand that she has to limit the invitees. None of us should speculate why some were invited and some weren't, for all we know she might have put all names in a jar and picked names.
All in all, I think it's kinda sad that we are so programmed that someone is doing something nice for the holidays and all we can do is find fault in how she went about it.
Think of it this way: every year your boss gives you four tickets to a local baseball/football game - the sky box, the whole nine yards: free food, free drinks, full service. You can only take three people because you can't buy more tickets. You have four very good friends that would love to go, and no matter who you choose you're going to upset one of them. Do you decide not go at all just because one person can't understand that you're limited to three of them? So they get to go next year and someone else stays home. Wouldn't it be rude of that one person to show up and expect to get in when you didn't invite them? I say this because I do occasionally get tickets to a baseball or football game (yes...skybox suite), and of the 3 friends that I have, I can only take one. There's always someone who whines to me about not taking them. Usually, that person won't get invited the next time, either. Who needs that?
It does seem that the party host throws one helluva party for so many people to feel left out and for all the hard feelings that are expressed! One should be so lucky! When I have a party I invite about 20 people and usually a dozen show up...which makes me feel like crap because I could have invited 8 other people who probably would have shown up!