Why would being at sea be any different?
I don't know. I guess my response would be, "It wouldn't"; I don't believe I would factor "at sea" into this at all.

I'll be the first to admit that maybe the question of "How obscene were chanties?" is not a very productive one. "How obscene were sailors' songs?" or maybe even "How obscene was sailor culture?" would give more to work with. My own task (FWIW) is addressing chanties specifically. It's a strange parsing, but I'd explain it by saying that the focus is not on the broader and more fruitful topic, "obscenity in song" - it's on chanties (and their characteristics, history, etc), within which a sub-topic comes about about how obscene were their texts.

I think this leaves out forecastle songs and such - indeed, it should (!) be pretty simple to disregard forecastle songs, so as not to corrupt the analysis of the chanties. I think there is a common wisdom nowadays that there are all these songs that were sometimes chanties and sometimes forecastle songs (and therefore cannot make a hard exclusion) . It's an appealing idea, especially since intelligent people know that lots of music/culture/etc is "fluid." Intelligent as that impulse may be, it turns out that the evidence, on the contrary, shows a clear divide. Examples of "crossover" songs probably number fewer than 10, even if certain dubious sources are to be believed.

Why do we sometimes tend to bring in forecastle songs at all? I assume it's because of the tendency to mix up the set of items "Chanties" with the set of items "Sailors' songs." But these sets just overlap. "Chanties" is not a set contained within "Sailors' songs" (and nor were they only part of the lives of men at sea); they overlap. Forecastle songs are not a significant part of the overlapping area. (And "forecastle songs," incidentally, were not limited to material in the traditions of the British Isles. Minstrel and other popular songs, with no connection to 17th-18th c. English bawdry, were at least as popular.)

My argument (i.e. in order to make an accurate assessment of obscenity in chanties) asks that the set of items, "Chanties," be further broken into overlapping sets of song-types. The key questions, I think, are: 1) Did the (A.) amount and/or did the (B.) nature of obscenity change over time (and if so, how/why/etc)? 2) How does the amount of obscenity break down in terms of those sub-sets of repertoire?