Answer:
Yes, membership in the Communist party will complicate admission as a U.S. permanent resident. Congress passed a law generally making inadmissible any applicant for immigration who is or has been a member of, or affiliated with, the Communist party. The lengthy processing time is probably related to investigating whether your parents are an exception to the general inadmissibility. There are two possible exceptions that might apply. At the interview did your parents explain that they became Communists as an operation of law when they were under 16 years of age? Did they explain that becoming Communists was to obtain employment, food rations, or other essentials of living and that becoming Communists was necessary for such purposes?
Your statement that parents were Communist bankers tells me that they are currently Communists. Therefore the third exception would not apply. The third exception requires that membership terminated at least 2 years prior to filing the application.
