Yes, a resource line the UART, because its usage by a task is not naturally atomic, needs protection.
Note, the SETUP for the uart is very likely not going to be changed, because the UART will almost certainly be physically connected to a line that will have a single defined protocol (baud rate, character length, etc). The protocol might have sequences that negotiate a change in that, but tasks will not be change that just by connecting.
The MESSAGES being sent over the link, may well need protection, so they go out as a whole, and nothing can interfere until that communication is completed.