Certainly, people living in the 11th century in Scotland would have believed in prophecies and omens. This is why, in the play, Macbeth and Lady Macbeth are so willing to believe the Weird Sisters' statements. However, many people living during Shakespeare's time would have been somewhat less willing to believe in prophecies and omens, and so Banquo would appear to be a much more modern character to Shakespeare's audience that the Macbeths.
Further, the omens that the Old Man and Ross discuss in Act 2, Scene 4, would be quite believable to Scots living in the 1000s. The Old Man talks about "A falcon, tow'ring in her pride of place, / [who] Was by a mousing owl hawked at and killed" (2.4.15-16). In other words, an owl (a bird associated with witchcraft) has attacked and killed a much stronger and more powerful falcon (a bird associated with royalty). Such a sight would have been terribly notable for them. Moreover, Ross mentions the fact that "Duncan's horses" rebelled and the Old Man says that "they eat each / other" (2.4.23-24). This unnatural occurrence appears would likely be read as symbolic of those who were formerly loyal to Duncan turning on one another.