That’s kind of an odd line to draw. You realize that more than homosexual acts are sinful. Sexual thoughts willingly entertained are grave matter for everyone. An unmarried couple engaging in a “loving, very close relationship” that involved heavy petting, passionate kissing, cybersex, sexting, or other kinds of brinkmanship are playing with mortal sin. So it’s hard to see how two homosexuals can have a “loving, very close relationship” while remaining blameless and chaste. It’s hard enough for heterosexuals to do when they are dating before marriage.
Since a “loving, very close” homosexual relationship cannot lead to marriage, they should be discouraged from the get-go as disordered. As a husband, I would not want my wife to have a “loving, very close” relationship with another man, I would certainly wonder what was going on there, and ask her to consider if she was truly committed to a marital relationship with me while developing that kind of bond outside the marriage. Even if she were committed and blameless, how would I know this other man would be respectful of her and our marriage vows?
That’s not to say that all close relationships should be discouraged. Parameters and boundaries can be set and observed in trust and respect. But when one person is romantically/sexually attracted to another in a situation where marriage is not an option, both of those people, as Christians, should be extremely scrupulous and circumspect to ensure that nothing unchaste transpires between them.
And for most people, that means steering well clear, keeping the person at arm’s length, never being alone together, keeping physical expressions to a minimum. If two people can maintain a “loving, very close relationship” without it ever being tinged with mutual attraction, or spousal jealousy, then they are much stronger than I am.