This is admittingly more topical with the Israeli and Jewish side than the Austrian.

I would like him to know and acknowledge his cultural background, the same as I would like him to be able to speak Hebrew (at the very least so he could speak to his grandparents and extended family). And I don't see anything negative in that, there is no limit of having only a single identity.

I also don't see what genetics have to with it. Indeed my grandparents had to flee Europe for similarly phrased reasons (being ashkenazi didn't help them at the time) and I find them just as distasteful now as then.