My gut feeling is that in most cases, a private club that allows only those with German ethnic ancestry or only those with Italian ethnic ancestry while excluding other whites as well as non-whites would be "ok", while a private club that allows any whites while excluding non-whites would not be "ok" (in a region where neither Germans nor Italians are a majority, but whites overall are a large majority).
I think there is a difference between a club that allows 15% but excludes 85% of the population based on ancestry vs. a club that excludes 15% but allows 85% of the population based on ancestry. I think the latter is more harsh for those who are excluded.
A rough analogy using kids:
A) First-grade class with 20 pupils; 3 of them get together for a party that excludes the other 17.
B) First-grade class with 20 pupils; 17 of them get together for a party that excludes the other 3.
"A" seems like no big deal; "B" seems unreasonably unkind (barring exceptional circumstances).
I agree with your other examples; but I think the black club vs. white club thing is different, for the reason explained above.