The appeal judgement made it absolutely clear that a protected belief can be discriminatory, and that acting in a discriminatory manner on the basis of that belief can be illegal.
This statement is correct.
No, a belief can be discriminatory. You are still entitled to hold it. You just can't act on it. Again, the judgement made this explicitly clear.
This statement is wrong.
If your second statement was correct, no religious person could manifest their beliefs, and neither could many other people who hold perfectly legal views that discriminate against others in one way or another.
It is perfectly legal for instance for a Nigerian immigrant into the UK to believe that only other Nigerian immigrants can understand their situation. And it is perfectly legal for Nigerian immigrants to found a community enterprise that restricts both its membership and its services to Nigerian immigrants.
This is lawful discrimination on the basis of the protected characteristic of race.
It is perfectly legal for a fairground to discriminate on the basis of age. It is perfectly legal for a gay club to discriminate on the basis of sexuality. It is perfectly legal for an antenatal course to discriminate on the basis of pregnancy. Etc
UK law differentiates between lawful and unlawful discrimination, so yes, you absolutely can hold a discriminatory belief and you can act on it. Whether that act amounts to lawful or unlawful discrimination is something the Equality Act and its regulator, the EHRC, help us with.
The judge in Maya's case included those paragraphs on harassment to explain that while believing that sex matters is a majority view in line with the laws of the land, you cannot deliberately use sex-based pronouns to describe a colleague or a customer when they have expressed a preference for other pronouns.
There would have to be a judgement as to whether this only applies to the immediate work and service delivery situation, or whether you could accurately describe a colleague or a customer with the corresponding sex-based pronouns outside of work or service-delivery in public, such as on Twitter. I would expect that a judge would hold that you should not do so.
However, it is absolutely allowed for a person to use sex-based pronouns for people in general. Otherwise the appeal judge would not have ruled the way he did.
As Maya did not refuse to use preferred pronouns at work, and there was no evidence she ever did presented by her employer, and as she had no colleagues she was working with who identified as trans, I am surprised that you are so sure lots of evidence exists about Maya doing this at work.