And when Claudius worries about "the great love the general gender bear" towards Hamlet (Hamlet, IV.vii.18), there is a similarly general sense of "common people". "The Phoenix and Turtle" has a further example: a crow is described as having a "sable gender" (line 18) - black offspring. The sexual sense emerges in the verb, when Othello talks of "a cistern for foul toads To knot and gender in" (Othello, IV.ii.61): here the word means "copulate".
But in the handful of other instances in Shakespeare, the noun has a much more general sense: "kind, sort, type". This is the sense required when Iago, talking to Roderigo, compares their bodies to a garden: "supply it with one gender of herbs or distract it with many" (Othello, I.iii.320).