I don't have any issues with the LGB aspect of it, although I believe the T+ aspect is currently a threat to women's rights.
If the rainbow was still just for the LGB and I was told to wear a rainbow lanyard, I would probably do so without thinking too much about it.
But it would still be weird if I did think about it.
Why this group? Why do our employers want to make everyone demonstrate visible support for this particular group, rather than disabled people, ethnic minorities, homeless people for example?
Whilst I don't doubt that homophobia still exists in our society, all the gay people I know are educated, affluent professionals in monogamous same sex relationships. A lesbian couple I know have recently had a child using a sperm donor and live very similar lives to me and my husband, except one of them is a woman. A gay couple I know have moved to the countryside and have an envy-inducing Instagram account filled with pictures of the amazing house they are painstakingly renovating, their extremely spoiled cat, and delicious things they have baked, broken up by regular fancy holidays. I don't see these people as oppressed minorities, I don't believe they see themselves as oppressed minorities or want to be thought of in that way. They want to be seen as perfectly normal couples, just like couples in a heterosexual relationship.
Of all the people I can think of that I might need to publicly demonstrate my support for to raise awareness of the struggles they face in life, those people are a pretty long way down the list.
And to be honest, I think if the rainbow flag was still just for the LGB, nobody would be forced to wear a rainbow lanyard.
It's the trans stuff.
By forcing you to wear a rainbow lanyard, your employer is sending you a very clear message that they won't support you if you object to a transgender male in the women's changing rooms. They're saying, "This organisation believes in gender woowoo, and if you don't, keep your mouth shut or leave."