The reason these conversations usually don't go anywhere is because there simply is not a morally neutral ground. Everybody has a point of view they think is right, and everybody judges at some point or another. The Christians usually get pigeon-holed as the judgmental ones, but everyone else is judging too, aren't they?
But, I will offer some insight as to where I stand on this issue, and why I believe the way I believe. I don't expect you to agree, I'm not putting my beliefs up for debate, but I want you to understand where I come from on this issue.
From a "common good" standpoint, I would ask "What is good for our culture? What is good for our community?" First, homosexuality is an activity that is inherently dangerous and cannot be made healthy. It carries health risks that may be reduced, but cannot be entirely avoided. Additionally, it can also put people at risk who are not engaged in that activity. Since it cannot be made healthy, and it puts others at risk, it seems to make sense that, as a community, we ought not do anything to encourage it. I wouldn't suggest actively discouraging homosexuality, but at the very least, let's not go out of our way to encourage it.
A more internal feeling is this: I don't feel uncomfortable simply because someone is homosexual. I've had several gay friends and co-workers. Some are likeable, some are not. I treat these persons individually. They are human beings that should be treated with respect, should not be bashed or called names, and should be given the same rights that any other citizen has.
Homosexuality is unnatural and immoral. This is not a personal preference, but a personal conviction. If you want reasons why I think so, I'll be glad to give them to you. This is my moral, cognitive conclusion about homosexuality. The way I feel about homosexuals and what I think about homosexuality are two different things. I don't confuse the two, and neither should you. I don't hate gays, all legitmate Christians should not hate any individual, but I do have a personal conviction against the act itself.