I've never understood the need for the rainbow lanyards within the NHS. If the only way LGB(and I'm even going to add the T here) can feel safe in a healthcare setting is by seeing someone with a rainbow around their neck, the NHS has far bigger problems than is acknowledged.
If you work in healthcare it shouldn't matter what a patient's politics, sexuality, age or even criminal history is, you treat them to the best of you abilities with dignity and care. Doesn't matter how you personally feel about them. It's your job. And sometimes that will be hard - a racist thug verbally abusing an A&E doctor from Uganda, treating a head wound obtained on a far right demo, still deserves treatment (and I think healthcare staff need greater protections from patients)
No one should be displaying their political leaning at work. I'm private sector and we have a casual dress code but we're allowed nothing that makes any kind of political statement. I work for quite a "woke" (for want of a better word) company but we have clients and we don't want to upset them or lose business. If you're in a tax payer funded, public sector role you absolutely shouldn't be allowed to demonstrate your politics while at work (unless you work in a political role - even then, politicians need to act in the interests of all the constituents and shouldn't be showing bias towards specific sectors of the community)
Sorry that was much longer than I thought it was going to be.
TLDR: show up, do your job, leave your whole self at home.