You: "... my husband..."
Me: "You know, I don't think gay people should be married. Marriage is blah blah blah"
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By my reading of the OP "my" comment there would be prohibited. Now, I'm bringing politics (or religion - which I also feel is and should be banned at work) into things to talk about why I condemn you or oppose your marriage.
In other words, rather than explain exactly what political positions and discussions are permitted we should just not have political discussions at work. If you mention your husband, I shouldn't tell you my thoughts about marriage or homosexuality. Conversely, if I mention I attend a Mormon Temple, you shouldn't tell me your thoughts regarding Mormonism. Details (within reason) about oneself are fine, but political discussion based on those details are not.
Of course, it's possible I've misread the document, and if they do intend to silence homosexuals from letting slip any details about their life, or whatever, then I oppose their changes. I think all people should be equally free at work to talk about themselves and their lives where it is appropriate. This document is just setting the guideline that political discussions are not appropriate.