dnd 5e – Can you switch to the other Unarmored Defense by multiclassing?

PHB p164 states:

If you already have the Unarmored Defense feature, you can’t gain it again from another class.

So if I start as a Monk and gain the UD(Wis) feature, and then at next level up, take a level in Barbarian, can I switch to the alternate UD(Con)? Or am I stuck with UD(Wis), even if I take 19 levels in Barbarian?

I’m unclear if the rule is stating this or stating that you can’t use both at the same time, which I know.