It's a bit nuts, isn't it? Tennant and anyone else wearing this badge (much like the rainbow lanyard worn by some NHS staff) is clearly designed to send a message to gay, lesbian and trans people that they (the badge-wearing individual) won't hurt them.
But the message it really sends is "This is a dangerous world for gay, lesbian and trans people, where lots of people are out to harm you."
I don't think that's a wise message to be sending out.
For the most part, this isn't a dangerous world for gay, lesbian and trans people, at least not in the UK. Luckily, we've moved on from the days when being gay meant you had good cause to be frightened of being beaten up.
The real aim of this badge, it seems to me, is to signal your virtue. The person who wears it does not inconvenience themselves in any way, but they get to show the world what a good person they are.