Are underarm serves fair in tennis? If so, why are they looked upon as a means of disrespect?

Underarm serves are completely fair in tennis.

The act of starting a point is very deeply rooted to the "ritual" of performing an overhead serve. Hence a player always expects to return an overhead serve. Consequently, underhanded serves have the benefit of surprise.

The overhead serve has a reason for being so common: it is far superior to the underhand serve in terms of difficulty of returning. The technique is designed to produce a much longer kinetic chain than underhand serves. Also, the point of impact for overhead serves is much higher than the net, allowing for better trajectories. Thus, the element of surprise is the only benefit to underhanded serves.

A professional serving underhanded would be somewhat analogous to a good free-throw shooter throwing underhanded: he can do it "properly" and yet chooses not to. The fundamental difference is that the element of surprise in an underhanded free-throw is meaningless, while in tennis it greatly affects the returner.

The reactions you cite are essentially a consequence of being caught-off-guard by a technique which, in terms of quality-of-shot alone (disregarding the mental aspect), is objectively far inferior.