This is by way of a follow-on to my last post.
Self-denial, in the modern psychological sense of that term, I do see as a potential good. I see it as a corollary of the 'self-control' which is a fruit of the Holy Spirit (Gal 5). I understand it to be the suppression or elimination of one facet of our nature in order to facilitate the development or growth of another facet which is even more important. So, to take a trivial example, refraining from extra chocolate pudding in order to preserve bodily health is a form of self-denial in this sense - bodily health being more important than the pleasure to be gained from the pudding.
In other words, the self-denial is not an ultimate good but an intermediate good - it is something which transitions to something else. Where my suspicions are aroused with the language of 'self-denial', and the equating of this with 'taking up our cross' is that I see a punitive and sacrificial theology behind it, by which self-flagellation is seen as a form of spiritual purification. I do not see it as an accident that those who are most concerned with this question are also most associated with the doctrine of penal substitution. That is the nature of the God that they worship, whereas I believe in a God who desires mercy and not such sacrifice.
So in the specific context of discussing gay relationships - and hetero ones come to that - I think that what I would most want to emphasise is that nobody on the outside can actually judge what is going on on the inside, save by some expression of the fruits of the Spirit mentioned earlier. It may well be that for some people, a denial or suppression of their sexuality is indeed of God, for such suppression enables them to become more the person that God originally created them to be. Yet for another, it seems equally plausible to me that to not deny themselves but instead to enter into an emotionally intimate and loving relationship is itself what will enable them to become the person that God is calling them to be. I don't think anyone can rule from the outside which is the best path for a particular person to take (a wise spiritual director might help a soul to make that decision for themselves perhaps). Of course, this ties in with one of the least-listened to but most dominant aspects of Jesus' entire ministry - Judge not.
My principal point, then, is not to say that 'self-denial', in the modern psychological sense of repressing desires, has no place in the life of the disciple. I do not believe that, and, indeed, I see that form of self-denial - if integrated with a wider theological understanding of the nature of God and what it means to be a creature - as a holy endeavour. Yet I would still maintain that there is a difference between this and 'taking up our cross' despite what would appear to be a superficial similarity of language. I see the taking up of our cross as essentially about enduring the hostility or criticism of a wider society when we choose to follow God. It is not about this psychological repression - unless, of course, that psychological repression is itself driven by social disapproval, as has no doubt happened in myriad situations, especially sexual ones.
So, to sum up: self-denial has a place in the life of discipleship, especially when theologically informed, but it is not the same as the taking up of a cross. Taking up our cross necessarily means accepting and enduring the rebuke of society, in all its various forms. The cross is imposed upon us by a sinful and adulterous generation, it is not something that we choose in order to get closer to God.