There was at least one episode where Elaine’s non-Jewishness was a major plot point. A series of Jewish suitors found her irresistable simply because she was a shiksa.
I guess a history of pogroms makes you leary of any gentile asking you too many questions about your Jewish heritage, but it’s a fair topic. Unless the individual bringing it up has a proven track record of antisemitic behavior or is targeting you for conversion. Short of that, your religion/heritage is a completely fair topic of discussion. As is that of the person asking you all the questions. And as for his being a conservative… Are political conservatives any different from political liberals in this specific regard?