Here are some private kiddush scenarios:
You just had a baby girl and you want to make a nice hot kiddush. On a given Shabbos about 200 people come to Shul and you must use an approved caterer for a hot kiddush, which will set you back over $1,000, which is not in your budget. So you chose to have a private kiddush in your home. The cost is at least half the price, and although it might be more crowded, it’s also more intimate and personable. The problem is that people who did not get a personal invite might be offended, which is the opposite of your intent in throwing the kiddush and sharing the Simcha.
When I was in Ramat Beit Shemesh a few years back, my friend’s Shul had a small kiddush after davening. The participants would rotate bringing small snacks and a bottle for a L’chaim. Although anybody could join, the group was about 10-15 men, and was somewhat exclusionary.
In our Shul, we’ll occasionally get together for a l’chaim and some chips and dips after davening. We once had a 10 minute kiddush, with a l’chaim, 2 divrei Torah, and some light food. These impromptu kiddushim are open to everybody, but because of their nature, invitations are usually extended to a small group.
A few years ago, our second cousin’s family spent their last Shabbos in Kew Gardens Hills, before they make Aliyah. We decided to make a kiddush in our home for their friends at the Yeshiva where he was learning. It’s not Shul related at all. However, I wouldn’t be surprised if somebody got slightly upset, because they heard we had a kiddush and didn’t extend an invitation to them.
In the above scenarios the participants have a right to make a kiddush, but nonetheless people do get offended. Most people get past it, as they do if they’re not invited to a Bar Mitzvah or Chasanah, but it’s unfortunate that in the friendship building Shul environment, some connections get weakened in these private kiddush scenarios.