Do squatting exercises irritate hemorrhoids?

Possibly: Any exercise that pushes blood into the anorectal region can make hemorrhoids more prominent. In general, the quick motion of squatting probably won't effect too much unless you involve heavy lifting.

Yes and anything: Else that increases intra abdominal pressure, such as protracted standing or sitting, straining with constipation or voiding problems, weight lifting, sit ups. Also alcohol.

Very much can: As anything that results in significant straining can exacerbate hemorrhoids.