King’s ties with the Communist Party are murky, and any reliable information is still sealed up either way.
There is a great deal of speculation - probably because “we are known by the company we keep”. As at least two of King’s closest advisors were known communists, one can’t help but at least speculate.
Of course, King was willing to work with pretty much anyone who was willing to stand up for civil rights - and the Communists were among the loudest supporters of civil rights.