> As a registrar Google is serving the public and I doubt you can deny someone this service in a moral sense.

Actually, you can deny anyone except protected categories.

> Can a doctor deny to treat them if they end up in his office for serious injuries?

Yes, the doctor chooses not to treat patients with the illness or injury you suffer from.

> What if all registrars deny them, is it morally right to effectively erase them from the internet for simply expressing their thoughts?

Nobody is being erased from the internet. Also, they can open their own registrar system.

So no, there's no obligation for Google, or any other registrar, to host their information.