From a legal viewpoint, the answer is dependent on the complexity of state laws[1]. What a website owner can do with a website in one country obviously differs from what they could do in another country. Most countries have very weak anti-discrimination laws, and if they do exist, they typically only apply for very specific purposes such as employment discrimination based on age. These limited laws tend to be near impossible to enforce short of someone self-incriminating themselves. In some countries however, an example being Norway, laws against discrimination can be very strict and routinely enforced to the level of requiring all website owners to implement WCAG 2.0 at AA level[2].
From an ethical viewpoint, the Universal Declaration of Human Rights[3] states in Article 2:
"Everyone is entitled to all the rights and freedoms set forth in this Declaration, without distinction of any kind, such as race, colour, sex, language, religion, political or other opinion, national or social origin, property, birth or other status.
Furthermore, no distinction shall be made on the basis of the political, jurisdictional or international status of the country or territory to which a person belongs, whether it be independent, trust, non-self-governing or under any other limitation of sovereignty."
"Everyone has the right to freedom of opinion and expression; this right includes freedom to hold opinions without interference and to seek, receive and impart information and ideas through any media and regardless of frontiers."
[2] https://www.uutilsynet.no/english/about-us/903
[3] https://www.ohchr.org/en/human-rights/universal-declaration/...
As a consultant, this would mean I can't turn down a client. Ever. It doesn't matter if I have higher paying offers, moral objections to what they want built, or silly just don't want to work with them.
This type of blanket declaration of freedoms can only extend so far as another person's rights aren't infringed upon. I the consultant example, my right to decide how I spend my time and value my work should be protected. If I can't discriminate for any reason because it could be deemed "[an]other status", my life can be wrecked because anyone asking for my services are owed good faith effort and I can't legally decline.