"A gay" is not offensive. The implied word is "a gay person" which is a perfectly fine thing to say.
The effect of saying it that way is a bit lighthearted which I suspect is what he was going for.
No one else has to say it, but that does not make it offensive. Similarly, while a country might want to move towards a particular usage for their name, or a company, whatever - that does not mean that the fact that many people continue for some time to use the older version are being offensive. Changing language takes time. The Kleenex company have tried to get people to say "tissues" for decades.
And as someone who spends a lot of time in universities, I think Murray is completely right about them at the moment. In fact so much so that I think their continued existence is not a sure thing if there aren't changes.
As for bringing your whole self to work, I think there is a clear space between talking about your public life (I went on a date yesterday with a bloke from Australia, my wife and I just bought a two-seater bike,) and specifically talking about your sexuality (I am sexually attracted to men/women/frogs in go-go boots.)
Yes, you could infer the second from the former. But while it is often ok to mention the former things in many workplaces, I think there is rarely reason to talk about the latter and it's often inappropriate. There is not a hard line on this, there is a grey area for sure, and not all workplaces are the same, so it's difficult to have a one size fits all rule. But that to me is the most basic general principle - is what I am saying part of my public life or stuff that is more directly about my private life - I have a wife vs who I like to have sex with.
Because as soon as you are saying, who I like to have sex with, for some people that includes, I like to have sex with frogs in rubber suits, and I don't think that should be seen as any weirder than Greg who is married to a guy.