I think you're right. It's "unlawful" but handled civilly.
While looking up the relevant law, I looked through the Civil Rights Act of 1964 which prohibits employment discrimination on the basis of sex and various other things, and discovered that there is an explicit exception written in to the law for members of the Communist Party. So you can totally discriminate against any commies who might try to work for you. Not really relevant here, but so weird I just had to share.
Jeez, the Cold War was a strange time. The exception seems especially weird since political party affiliation wasn't a protected class in the law to begin with. I guess that meant you legally could say, "We only hire non-Communists, regardless of sex/race/religion/...; and white Communist Jain men of Estonian origin."
I wonder if it was just a "safeguard" against members of CPUSA claiming their membership was a religious affiliation.
It sounds like it was an amendment introduced by a confused lawmaker who wanted to make sure the law wouldn't stop companies from firing Communists. The amendment was then accepted on the basis that it didn't make any difference (since as you note party affiliation isn't protected in the first place), so it wouldn't do any harm to include it.
While looking up the relevant law, I looked through the Civil Rights Act of 1964 which prohibits employment discrimination on the basis of sex and various other things, and discovered that there is an explicit exception written in to the law for members of the Communist Party. So you can totally discriminate against any commies who might try to work for you. Not really relevant here, but so weird I just had to share.