Simple.
Include "critter holes" at regular intervals.
At ground level, large enough for rabbits, snakes etc to traverse but too small for humans.
I don't think we can have a fence.
People on the other side will find some way to abuse those "critter holes," as in, pushing through bombs, incindiaries, whatever. If the "Mexican" threat is to ugly-up the Mexican side of a wall with uglyolegraffitti (who cares), then they'll be looking for other means to vandalize, to state the obvious.
Interesting that they'd resent a wall and not express years of gratitude for all the free stuff.