Yes, true and false with AND and XOR form a mathematical ring [0]. Still, OR is also an additive operation. IMO one could give OR and XOR the same precedence.
On the other hand, there is no strict need to have a dedicated boolean XOR operator, as it works the same as = (equals).
On the other hand, there is no strict need to have a dedicated boolean XOR operator, as it works the same as = (equals).
[0] https://en.wikipedia.org/wiki/Ring_(mathematics)