They do not have a right to your identity. But I do not see why people have an absolute right to use a business without providing identity either. If both parties agree, then they can exchange info.

The government is using 2FA SMS as your identity (for government services themselves), effectively offloading their liability into the mobile operators. But not really, because the mobile operators are not liable either. So as a little person, you are screwed all around.

If the government were to make an electronic identity, which it needs to for its own services, it might as well be accessible for all so you do not have to trust private businesses with it.