A friend of mine from high school--more correctly, a Harvard-attending semi-notable journalist friend of mine--attempted to engage productively with Jon Chait's essay on microaggression (or something: I learned long ago how to sniff out and avoid that which reeks of this is not going to lead to a productive discussion) by pointing to various true and accurate facts about what it's like to be a white male heterosexual in the United States of America if one is aware that it is such a thing to be one of those, and not neutral experience. It did not go well.
As one of those white men, here's (some of) what I've learned about interacting across boundaries. It is important, first, to recognize that not all spaces are yours. You may be interested in them, you may want to learn from them, you might see them making errors that could be corrected, but you will always and fundamentally be an outsider. That is fine. Remember that people are not always looking for allies who have disagreements with them, even if those disagreements are reasonable and limited and could be worked out in dialogue (see Tim Burke on this topic). That is also fine. There are some situations in which dialogue, even in the best of situations, will prove to be unproductive. That's fine, too. You're dealing with neither more nor less than the standard burdens of having a conversation in a world where people disagree with each other. You don't know everything, but neither does anyone else. You're not obligated to give up an argument because someone else is making a different one (even if that argument is an emotional appeal, even appeals based on life experience), but you should be careful to always be testing what you believe and trying to find potential things you may have overlooked. That is neither more nor less than the standard ethical duty of being a human.
(There are a lot of books out there that talk about experiences far removed from your own. It's probably a good idea to read widely from them. This is true for everybody.)
If you find yourself in a position where you are not welcome in a particular space, or find yourself having an unproductive conversation, it's worthwhile to remember how much of the very important work happens when no one is arguing: in the things we teach our children, in how we treat friends and strangers, in the attitudes we demonstrate and in what we expect from others. In The Origins of Totalitarianism, Hannah Arendt ends by quoting Augustine--initium ut esset homo creatus est, "that a beginning be made, man was created"--and relying on the hope presented by every new-born person as the real vehicle for change. That seems as good a basis as any around which to work.
(There are some supplementary issues for those of us who teach, or have taught, in the obligation to create a classroom that is theoretically and in practice open to the spectrum of opinion, which requires a careful selection of texts and an authoritative hand in guiding discussion to create a space where people are allowed to disagree--to be wrong--without fear of their grade or the immediate reaction their comments may inspire. This is true for conservatives and liberals, the religious and the secular, and every socioeconomic and ethnic group. We were all once 18-22 and probably held at least some views we wouldn't agree with today; certainly we didn't know as much then as now. If people are being driven out of a classroom, as in some of the stories that have floated around, then it's an absolute failure on the part of the instructor.)