Hi,
It's a little tricky to explain why these tenses don't always seem to fit together, but here are a few brief comments.
1. This was not the first time that an artist had been rejected by the establishment... To me, this seems the best of the 4.
or
2. This has not been not the first time that an artist was rejected by the establishment... The second 'not' is wrong. The present perfect does not fit well here. However, I wouldn't say it's wrong. But is sounds awkward to me.
3. This has not the first time that an artist has been rejected by the establishment... Do you mean 'this has not been the first time. .' ? The double use of the present perfect again seems very awkward and hard to understand..
or
4. This was not the first time that an artist has been rejected by the establishment...
The simple past seems to indicate we are talking about the past, so the present perfect seems out of place.
Best wishes, Clive