But there’s no halachic basis for rejecting converts who say they accept everything (and who have a sponsoring rabbi to vouch for their observance).<e/m>
First I thought you were saying we are supposed to accept as a ger anyone who “says” they will accept everything. That is obviously not correct.
But then you qualify by saying “and who have a sponsoring rabbi to vouch for their observance”, by which I suppose you are adding that we are supposed to also determine that they probably are going to actually accept everything.
So then we agree. And we should also agree that if a certain rabbi has been vouching for candidates and is obviously terrible at it based on his track record, we should stop accepting his vouchers.