I think that all parties should talk to people from all other parties. Their views may differ, but there is no reason why they shouldn't get along, and IMO it is very important that people can see the alternative point of view, even if they are never going to agree with it.
For one thing, it is impossible to construct an argument, without knowing what the other side is likely to throw at you, and for another, it is a fool who thinks that they, and only they, are always right - sometimes there are compromises that can be made whilst still achieving your goals.
I think that this is true of party leaders, other supporters (eg the Mayor in the OP) and of ordinary people in everyday discussions.