On the other hand, these are not exactly the "eastern European hordes"-German and upper-class Bohemian/Moravian/Austrians would be largely well-off, educated professionals and assimiliated. So they could well be more politically acceptable.
One would hope! And we don't really have any historical examples of a largely well-off, educated ethnic group making its way to the US, so who knows? (Maybe the Parsis of London are the closest example, but then were they arriving in similar numbers?)
But it's hard to lose betting on discrimination prevailing in the past, unfortunately, and the non-Christian factor is hard to ignore, no matter how well-off they are. I think a lot would depend on settlement patterns and rates as they relate to specific events. Like if the Germans have rolled out a worse version of their prewar behavior before the Olympics? That could increase support for taking them in.
To me it's more interesting to think about how it might affect local demographics where they chose to settle. We'd likely just get marginally higher Jewish populations in areas of already significant settlement, especially since we have evidence of a lot of retained family ties IOTL between American and European Jews through the 1940s. From this view it seems like 300,000 is pretty easy for the country to swallow. If they all settled in the Mid-Atlantic, they'd barely add 1% to the population. If all of them lived in NYC they'd up the foreign-born population by about 15%; significant but not a deluge.
Of course if they all tried to settle in just the Jewish neighborhoods of NYC, that could be a problem (I don't know exactly which neighborhoods we're talking about in the 1930s). Could be an interesting facet of a quasi-New Deal public works program: new dense high-rise neighborhoods for the recent arrivals. The Jewish Projects?