Do Schmitt-trigger specs give requirements to avoid metastability?
Such considerations simply don't apply to the normal applications of Schmitt triggers. Schmitts are generally used where the input slew rate is much less than the output slew rate. With a slow input, the trigger point is not clearly defined, being affected by other factors such as noise and feedback from the switching transients as the output changes. Once the trigger point is reached, the positive feedback pulls the threshold quickly to the other level, and oscillation is prevented. 

However, it is entirely true that Schmitt triggers exhibit metastability, and this was demonstrated in 1977/1979 by a series of remarks in the  IEEE Transactions on Computing, by E.G.Wormald and Thomas Chaney. See http://fpga-faq.org/FAQ_Pages/0017_Tell_me_about_metastables.htm for a discussion of the subject.

So basically, Schmitt triggers are not much use for fast signals. For slow signals, they are very effective, but in these cases the low frequencies make metastability much less of a problem, since high sampling rates don't make sense, and there is relatively more time for metastable conditions to resolve themselves.