“Liberal Priest” = “Priest I don’t like”
I wouldn’t presume that everyone is using the term in the same way. I think it’s unfortunate that we use the same adjectives for politicians as we do for priests and theologians.
On these fora, I think the term is used most often to describe a Catholic that believes and/or teaches something that goes against Catholic teaching. For example, someone who advocates for women priests, gay marriage, etc.
When discussion turns to the liturgy, sometimes the definition changes somewhat to refer to any priest who doesn’t follow the rubrics (or at least the poster’s recollection of what he
thinks the rubrics say).
Frankly, I see no reason to use the adjective for a priest unless he chooses to self-identify as such. It is generally more useful to stick to whatever the discussion at hand is about.