Well, this is a very difficult topic within our culture, because we have lost sight of the distinction between friendship and marriage, and because we do not often think about the different kinds of love.
Friendship is a very distinct kind of love, which involves personal (not sexual) intimacy, a genuine enjoyment of the other person’s company, common interests, and so on. It has the unique characteristic that it is love for that person’s unique characteristics. (Compare universal love, the kind of love we are supposed to have for all people, regardless of their characteristics.) In this is replicates a certain aspect of God’s love, which is both particular and universal, and that is a very fine thing. Friendship is an important and rewarding part of life for almost all people, at least at some point in their lives. It is also possible to have more than one friend - it is not exclusive.
Marriage has not been traditionally understood, within Christianity or without, as necessarily encompassing friendship. An integral part of marriage is the vow of love, which is a duty, and in a way more like universal love. We are bound to it even if we don’t “feel” very loving. Difference plays an important part in marriage. The bonds of marriage are tied up with sexuality, child-rearing, and a common life. Common activities, likes and dislikes, which are central to friendship, do not need to play a part. Not everybody is called to marriage, and many will never marry. And we only have one spouse, at least at any one time.
Now, culturally, we tend to encourage people to choose a spouse on the basis of something closer to friendship, as well as romantic love which has a strong physical component. This is not necessarily a bad thing, and friendships have often occurred in marriages that started out without them. But, they are not central to what it is, and when people forget that, it causes many problems. They often think, quite honestly, that the substance of the marriage has disappeared when friendship cools. Or they let the bonds of friendship stand in for the bonds of marriage - common goals and child-rearing.
Now dating or courtship is NOT friendship. It is one way of people getting to know each other with the end of marriage. The main focus should be on discerning whether this would be a person with whom you want to live a married life, and so you should be looking for the qualities as individuals and as a couple that would lead to that. And it tends to be exclusive, at least once it’s past the initial stages.
Perhaps this makes it more clear why a homosexual would not be able to date someone of the same gender without being in a contradictory position - dating is looking for a kind of compatibility or an end that cannot be.
Friendship on the other hand would be fine, even if some silly people call it “dating” which they certainly do at times if the friends are of the opposite sex. In fact I would say that it would be very important for a gay person to have friendships or loneliness would likely be a serious problem. The only difficulty would be where friendship started to lead to feelings of another kind. That happens with opposite friendships too though and there are ways to deal with it, though occasionally it means backing off from the friendship. I think it tends to be exaggerated because of our inability to differentiate between friendship and romantic love - it used to be much more common to see deep, intimate friendships among men; now people tend to assume there were sexual things going on because they can’t imagine anything else.
You might be interested in reading “The Four Loves” bu CS Lewis, which talks about the various kinds of love and their place and purpose.
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) and their subsequent sexual activity would not be sinful in the eyes of the Church.