Yes you can eat mussel beards because the mussel beards are edible and safe to eat.
However the mussel beards are not very tasty or appetizing so most people do not eat the mussel beards and instead most people remove the mussel beards first and then eat the rest of the mussel.
I've tried mussel beards before and to me at least they were gross tasting so I threw them out.
But you can eat mussel beards if you want too and you won't be harmed.
The rest of the mussel is what is more enjoyable to eat.
But different people like different things.
You can either remove the mussel beards or eat the mussel beards but you'll probably want to remove the mussel beards first.