I am a straight male, who has no qualms with the lifestyles of others.

That said, if a TA booked me into a hotel with that logo, they would never get my business again. I honestly probably wouldn't even give the hotel a chance, as I would interpret the "gay" logo upon arrival as being "geared towards gays." Unless that is what I was specifically looking for, I would be put off by it. As other have mentioned, many places have small token on the door or other specifying "gay friendly" which is fine, and I surely don't mind if the guy at the reception counter is stereotypically homosexual, but I would never book myself into a place that is clearly marketing to the gay lifestyle, just not my cup of tea.