apushatayid asked “Where does he imply there is something wrong?” (even if it is done outside a shul)
The answer is when Reb Moshe said…
“Therefore, you should distance this new thing of a bas mitzvah celebration, and not to encourage it”
“it is a matter of nonsense”
“the source of this practice comes from the Reform and Conservative”
“there is no basis to consider this a mitzvah matter”
“it is nothing more than a birthday celebration”
So clearly Reb Moshe was opposed to the entire idea, even if it wasn’t strictly prohibited to conduct in the privacy of ones home.