How might an individuals personal beliefs and perferences affect communication?

There are a lot of ways to answer this question, but the simplest is to give an example. In ancient Greek paganism, a daimon was a spirit, usually beneficial, and which served as a protector and guide to the individual. However, Christians later changed the meaning (and spelling) to "demon", a hostile spirit working under direction of Satan to corrupt and condemn humans. Obviously, these are too mutually exclusive and contradictory definitions and should a modern Christian and an ancient Greek broach the subject of theology.... Things would get sticky.

There are other forms of bias that can affect communication as a result of religion (the following are examples within Christianity but it should be understood that Christianity is not the only religion guilty of this): Eve was guilty of the first sin in Genesis and coupled with sentiments like those found in 1 Tim 2:12-15 which contributed to misogyny and how men communicate with women for thousands of years. Likewise, the crucifixion of Jesus "by the Jews" (it was the Romans, but that's another matter) led to wide spread anti-semitism.

The list goes on, but religious bias is difficult to overcome as it is something present (usually) from a very early age, as opposed to something that tends to develop latter in life, and can greatly interfere with how people communicate and with whom they communicate.