What would happen, governmental policy and public reaction wise? Surely the U.S. Government would not pass overtly anti-Semitic legislation, especially as the civil rights struggle is starting up. Unofficial anti-Semitic discrimination will definitely ramp up though.
I dread to think what the KKK et al will think they can get away with here against Jews
Certainly no legislation, it would be too easy to overturn as unconstitutional...though you might see vague references to "alien nationals" and the increasing implication that Jews were all
de facto Israeli citizens despite being American citizens as well. But it wouldn't be too hard to see Jews turned away from all government jobs, Jews turned away from the military, Jews having trouble running for office. At its worst, Jews might even have trouble with ordinary government bureaucracy. And such policies coming from on-high will encourage those policies down-low. Jews will never "become white" like OTL.
And once the Civil Rights struggle starts...hooee. Jewish involvement was already problematic for a lot of people, this is going to make it worse, and might make the entire project more difficult, even potentially leading to moderate African-American leaders shunning them (though Malcolm X will no doubt be happy to welcome them).
It's not clear to me how you can get that, given the relative poverty and unattractiveness of Israel as a destination and the relative strengths of the United States. Despite all of the undeniable anti-Semitism, the United States was arguably the safest country that large Jewish populations (in the range of millions) had ever enjoyed, and certainly was the richest ones.
The only analogue I can think of is the decline of the German Jewish population in the 1930s, which fell by almost half as a consequence of Nazi persecutions. I'm not sure that this analogy is especially useful, not only because this implies a degree of coordinated anti-Semitic violence in the US that I think unlikely, but because the German Jewish population amounted to hundreds of thousands and not millions as in the case of the US.
One mitigating factor is that as American Jews pour into Israel, Israel will get wealthier and more attractive.
And, right, the US wasn't (and in many ways isn't) perceived as much less antisemitic than contemporaries like the UK, France, Canada, Germany (in the 20s...). Getting American antisemitism to the level experienced today in France, for example, strikes me as very doable. Of course, Israel in 1950 or 1960 isn't Israel in 2015, but once the trickle starts, it might turn into a flood sooner rather than later.
All that said, this thread is asking about a relatively unlikely scenario. Definitely not ASB, but it'll take a little doing.