Honey mesquite is very prevalent in my area, and I have never heard of any plant parts being poisonous (the pods in fact are edible) and have never known anyone to have an allergic reaction.

Here's what a quick search turned up:
Mesquite is not known to be highly toxic. However, there are parts of the plant that can have adverse effects. When eaten, the seeds can cause digestive problems (Tull, 1999). Though the spines arenÂt necessarily poisonous, they may cause soreness ("Honey Mesquite"). The flowers are allergenic and the pollen can cause hay fever (Tull, 1999). The gum may also cause irritation (Kay, 1996).