Although Schmitt triggers are not usually regarded as latches with setup/hold constraints, a Schmitt trigger is functionally a sort of latch which is forced one way when the input is above a certain threshold, forced the other way when the input is below a certain threshold, and is expected to hold its value when the input is between the upper and lower thresholds. While the thresholds may or may not be specified in such fashion as to have a non-overlapping region between them, the fact that a device doesn't switch at a particular voltage but switches at a voltage near that would imply that the former voltage should be within the "hold" zone. For example, as given in
Table 7.5 of PDF
which guarantees 0.4V hysteresis, if device outputs high while the input sits at 1.2 volts, then goes low when the input rises to 1.3 volts and sits there awhile, it must remain low until the input goes below 0.9 volts. If the output hadn't gone low until the input rose to 1.5 volts, it could go back high as soon as the input went back down to 1.1 volts.
Because the Schmitt trigger is a latching device, it will necessarily be, like all latching devices, susceptible to being placed in a metastable condition. While an ideal Schmitt trigger would switch exactly once if given a signal which never deviates by more than +/- 0.2V (half the hysteresis voltage) from a monotonically rising or falling waveform, it must like any latch have input conditions which would induce metastability. Most latches and latching devices have designated setup/hold timings and promise that they will not go metastable unless those timings are violated. Do Schmitt triggers offer any guarantees, e.g. promising that a signal that crosses the upper threshold for less than some maximum "reject" time will not cause the output to switch at all, and any signal which crosses the threshold for more than some "capture" time will be guaranteed to cause the output to switch and stay switched? Are such guarantees documented anywhere?