No, it doesn't, but it might attack the aims of granting free speech. It may make people feel less free, or less safe, but it doesn't take away their ability to have their own say.
I think anybody should be allowed to say anything, and then people can resolve problems on their own. Rational people limit what they say based upon the environment. If someone asked me about my sexual identity in Alabama, I'd be unlikely come right out and say I am queer.
A much more convicing argument for Tenner's point of view is:
Hate speech should be illegal because it impairs others' freedom. If a group of workers in a male-dominated environment put up porn on the walls of the changing rooms, it may make the few women feel uncomfortable.
In the case of the living room with the person spouting racist remarks, there is a distinction between public and private places. In public: anything goes. (There, it might be useful to incorporate sgrove's idea of ideas vs just words.) In private, people have a right to control their own environment.