You have a couple of characters, Lucy (main LI) and Rose (secondary character, I wouldn't call her LI) who have a rather liberal concept of sex. But you can ignore both. Then you have the other main LI Mallory, who, apart from one with Lucy at the beginning of the game, before she started a relationship with the MC, only has sex scenes with the MC. I can't say if Amber, who has appeared little during the game, is a main LI or not (but according to the variables it seems that it is, since you can earn points with her and that only seems to happen with main LIs).
The game has two alternative routes parallel to those of the main LIs: you have ellie's (younger sister of the MC) if you use the incest patch. Or a route dedicated to the "sexual travel" in which the MC has sex with different girls in each world he visits. I haven't played this second route, so I can't pinpoint exactly what happens, but in the first you can prevent Ellie from having lesbian relationships (the Dev indicated that he has no intention of Ellie having an interest, sexual or romantic, with guys other than from the MC, so she will only have lesbian relationships and only if the player wants it). For now she can start relationships with Rose, Lucy and the older sister (can't remember the name). And if you have the incest patch you can establish a relationship with the big sister if you play the cards right. Neither of the two sisters has to have relationships with anyone other than the MC, or at least it can be avoided until now.
With Rose the MC doesn't establish any romantic relationship, but an exclusively sexual relationship can be started with her, in which she will continue sleeping with others (boys and girls). Personally, I'm not interested in this type of relationship and have avoided starting it.
Lucy is a main LI, but she has a few sex scenes with different characters (two antagonists, Mallory, and one no explicit scene with Rose), although if you listen to her thoughts she seems to have a crush on the MC. In either case you can ignore her romantically and go on a route with Mallory (or ignore both and stick with just Ellie or the sex trip, depending on which path you choose).
You can actually avoid having a romantic relationship with all the LIs (avoid having points with Lucy and Mallory and don't include the incest patch and you avoid all the LIs that the game has for now). But the sex travel is unavoidable if you don't include the incest patch. The purely sexual relationship with Rose can be avoided.
What you can't do is remove them from the game, whether you start a relationship with them or not, they'll still be in the game and fulfill their role (besides you can't avoid the sex "scene" between Lucy and the MC, although it happens off screen)
