a celibate asexual relationship like that would be little more than cohabitation with maybe some kissing. So, basically, roommates who love each other. That's kind of uncommon, and the Bible was written long before romance and sexuality were given orientations and whatnot, which are frankly just social constructs sometimes.
But in that case, I think it depends on how far they took it. You probably already know this, but we Christians believe that God not only gave a purpose for biological sex besides "provider of gametes", but also to illustrate the complimentary nature of male and female. A close friendship between two men or women can exist, and they can love each other and even kiss (kissing means different things in different cultures).
But the reason Christianity does not really approve of sexual activity in these relationships is not just because of natural law or the Bible said so--considering that the bible "said so" only a handful of times. The main reason is likely because God did not intend for friendships to necessarily become sexual relationships, and for a man or a woman to assume an opposite gender role as one person might sometimes do in same-sex relationships (though not all, of course, and fiction tends to alter cultural perception).
It can be inferred from various parts of the Bible that the man works hard and takes responsibility, while the woman nurtures, protects, supports, utilizes and values emotions Instead of just plowing through them, and manages internal affairs in the family. Does this work out all the time? No. Is every man or woman equipped for that sort of role? No, although I think this sort of stuff is for more than just parenting. But mothers and fathers are needed for children if they can physically produce them (infertility is another topic), and romantic feelings are fleeting for both gay and straight couples.
So as long as this hypothetical couple had no sex and re-assessed their relationship to determine whether it was really romance or just a close bond (such a thing exists, and nowadays our culture seems to think that romance is the strongest bond, but given that break-ups and divorce exists it clearly isn't), then it might be acceptable. But I'm ultimately not the judge. God looks at the hearts of people and exposes their true motivations.
honestly, a lot of times romantic desire might just be a longing for company. I have several times thought that I was "in love" with someone just because I wanted to hang out with them more, and then I assessed the situation and realizes that no, this person was not going to be a future spouse.
As for yaoi and yuri, that's fiction that tends to portray relationships like that for either self-insert purposes, sex appeal, or to explore the nether regions of same-sex relationships. But I don't think it's very indicative of real life, even if it is well-written. Although I wouldn't know, I have never sampled yaoi or yuri and probably never will.
I feel like you're ,misunderstating asexuality: it's not just a lack of physical intimacy, it's physical intimacy without the sexual undertones to it, from what I've been told and researched (briefly). Sex is where there's deeper intimacy, but intimacy in a physical sense can exist without sex, same as emotional intimacy with a couple that does have sex.
Again, this seems to misunderstand how sexual relationships work with homosexuals or even heterosexuals: it's not purely about complementarity of your sex, it can be just as much, if not moreso, about complementarity of personalities and such, which arguably aren't deterministic or absolutely limited by your sex or gender. Two people loving each other doesn't have to be about their sex, even if there is an unconscious drive related to that, even if not based in reproduction or a general understanding of nature as having the "selfish gene" to quote Richard Dawkins. A man in a same sex relationship with another man isn't technically being a "woman" unless you reduce the submissive role in sex to something that must be for women, which is silly, since a man can be submissive and a woman dominant, they're not mutually exclusive in terms of the roles they can play in a relationship, sexual or otherwise.
Certainly parents are required for children to grow up well adjusted, but I don't think the evidence is on the side of a purely gender binary structure for parenting in order for a child to not turn out bad, since children can have a mother and father, biological or otherwise, and still turn out terrible for entirely unrelated reasons.
At least you're being realistic in saying that both gay and straight people (among others, technically) can both be fleeting in their attractions, though I'd qualify that the term we should use here is infatuation moreso than attraction in a sense that leads to committment. Merely liking someone in that sense without the idea of committment coming to mind is something every person can be guilty of, sort of a violation of Kantian categorical imperative, since you're using a person as a means rather than an end
Romance isn't the only strong bond, but it's certainly presented as such more than others: One Piece, a manga about pirates, has a group of characters that, I'd say don't need to be implicated as having any romantic interest in each other at all, but merely are strong friends that have an equally strong bond that's been forged over time.
I don't disagree, though I've rarely had those feelings in the last 5 years, especially post college with failed relationship attempts (2 of the women I had any interest in turning out to not be interested in males in that way or outright never saw me in a romantic light)
There's bad romance of any kind and I can't speak about a lot of yaoi or yuri anyway, since I have a limited exposure to it myself, even with my best friend who's practically a fujoshi in the positive sense, albeit in my understanding, she's been more in the Western fandom, so there may be a separate term for that (shipping Supernatural characters, for example). Of course it's fictional and isn't necessarily meant to be a full representation of romance, but it's not like it should be avoided merely because you're averse to it in a sense that isn't based on literary criticism, but a moral concern. I read plenty of manga that invokes Christian imagery, for example, but that doesn't mean there's some cognitive dissonance.
