I don't know. Any raspberries that propogate from the roots are clones so will be exactly the same as the parent plant. Those you don't have to worry about. The fruit they produce depends on the parent plant.
But you can also grow raspberies from seeds. If the two different raspberries bloom at the same time, I'd think they could cross-pollinate and the resulting plant from the seeds would be some type of cross, not pure. Raspberries are self-pollinating so you don't have to have a different variety to pollinate them, like you do with apples.
I'd plant them anyway if you really want the different variety. If you have wild raspberries in the area or if your neighbors have different raspberry cultivars, they are going to cross-pollinate with them. You can't stop the bees. But I think the vast majority of plants that come up will be from roots, not seeds, so you should be OK. But I don't know for sure.