More or less, they do. The obvious difference is singular vs plural, but it really makes little difference in this context. I'll abstract it out a bit, which might be helpful:
- [People in a group] have a tendency to believe x about [people in a different group].
- A [person in a group] has a tendency to believe x about a [person in a different group].
- A [person in a group] has a tendency to believe x about [people in a different group].
Since you're saying that there is a tendency, that means that it's often likely that something is true, and whether you refer to an individual in that group or the group as a whole, the end result is the same, you're describing a generality about individuals in a group (otherwise known as a stereotype). In every case you are saying that many, but not all have this belief.