Yeah sadly you will find a lot of bizarre, belligerent people arguing to death about the precise definitions of all of these terms. I'm not someone who is going to die on these hills so no worries if nothing changes.
The only reason I think prostitution didn't raise a flag for me is because I think most guys assume a Male MC game with the prostitution tag is just him paying for sex, not necessarily pimping out his girls. Structurally this game has a lot of similarities to Secret Care Cafe, which uses both NTR and Swinging tags. Both hospitality management games in which the lead character shares his love interests with patrons, etc. Then you have Photo Hunt, which also has LIs get pimped out in a brothel but they only use the swinging and not NTR tag since it's all specifically engineered by the MC.
Since the Nat sharing stuff isn't prostitution, as it doesn't take place in the club (beach sex scene and even the threesome with Lilith is sort of swinging in a way), I feel like there's a justification for either ntr or swinging tags. I'm not sure in what direction the game is going, but there's also language about non Club girls with other men (like Shirley for example) so if there will be more sharing content, swinging or NTR (or both) would be applicable for sure.
That said, it's always a double edge sword, because while you may attract people like me, who are just looking for great sharing games, you'll also get people who either a) come in, see an ntr tag and say "Oh NTR? Pass." or b) people who see the NTR tag and spend 20 pages in the thread arguing about what technically constitutes NTR, which can be exhausting in it's own right.
No right or wrong answers here, either way I'm glad I found the game. It's awesome, for what it's worth I think the sharing is the best part of the game.