Why was "blacklisting" a problem in the Hollywood entertainment industry?
Blacklisting was not really a problem for the Hollywood entertainment industry as a whole. Instead, it was a problem for individual people in the business and for civil liberties in the US.
The blacklists were made up of people who were suspected of being communists or communist sympathizers. Companies would not hire anyone on the blacklists and so the careers of those who were blacklisted essentially came to an end. This did not harm Hollywood in any direct way as the movie and TV industry remained very profitable. What it did do was to kill the careers of some individuals and to infringe upon the basic American rights of freedom of speech and freedom of association.