What does that phrase mean in the following sentence. "Regressive taxes are applied across the board and on their face they seem pretty equitable."
The relevant entry in Wiktionary is
On the face of it: (idiomatic) Apparently; as far as can be seen or determined.
Thus, regressive taxes seem pretty equitable, as far as the author can conclude.
One can gloss "on their face" as "outwardly" or "looking from outside" - because when we look at some object from outside, we see only its "face" - its outer surface.