Even in Hollywood, there was a “blacklist” of entertainment figures that should not be hired because they were suspect for their role in support in communism.

I believe this sentence is confusing with the use of should. Do you agree? If so, what word or words should I use instead?

First of all, get rid of the wordiness.

http://grammar.ccc.commnet.edu/grammar/concise.htm

How about this?

Even in Hollywood, the practice of blacklisting became know. Entertainment figures were denied jobs because they were suspect for supporting communism.

Better.

What's the context that gives the reason for using the phrase "Even in Hollywood"? Why can't it just be "In Hollywood"?

Maybe this:

In Hollywood, the practice of blacklisting caused people to be denied jobs if they were suspected of supporting Communism.

(I'm not even sure "the practice of" needs to be in there!)

Yes, I agree that the sentence can be confusing due to the use of "should." To clarify the meaning, you can replace "should" with "were deemed" or "were considered":

Even in Hollywood, there was a "blacklist" of entertainment figures that were deemed unfit to be hired because they were suspected of supporting communism.

Even in Hollywood, there was a "blacklist" of entertainment figures that were considered questionable for their role in supporting communism.

Both alternatives remove the suggestion of obligation or necessity implied by "should" and instead focus on the evaluation or perception of these figures.