This is a good political question related to international politics and foreign policy.
To the question you linked, indeed both the questioner and some of the answerers (including me) made a generalisation that all the countries voted keeping their own political interest in mind. When so many nation-state actors are involved, sometimes we do make common sweeping judgements to understand something, despite knowing that it may not be applicable for everyone. There will definitely be some who are outliers with different political motivations.
But then, the question why that particular generalisation of states acting selfishly? Why wasn't the generalisation based on benevolent politics of good ethics and moral? Why didn't any answer say it was because all these nation-states genuinely believe that China was not committing any human rights abuses against the Ugyhurs?
The answer to that, partly, is public perception. When it comes to political players, the public in nearly all the countries look at them cynically. Sure, one may shed the cynicism for the political leader they admire, but the general public perception are that politicians are self-serving creatures who prioritise their own self-interest first.
Thus, when it comes to nation-states behaviours too, we tend to project these same cynicism.
That's one part of it.
The other is a political theory called the Rational Actor Model that can be used to determine how a nation-state made / makes a political decision, especially on foreign policy. Basically, this theory assumes that the leader of a state always acts rationally to achieve a particular, or a set of, goal(s).
The formal way of laying out the Rational Actor Model is by using four key concepts:
To determine the cause of a nations actions, one must analyze:
(1) the Goals and Objectives of the Nation,
(2) the Alternatives,
(3) the Consequences, and
(4) the Choice the nation made.
With these four concepts, one can analyse the nations leaders development of making a decision by using the RAM.
Now, what was the motion that China defeated?
The U.N. rights council on Thursday voted down a Western-led motion to hold a debate about alleged human rights abuses by China against Uyghurs and other Muslims in Xinjiang in a victory for Beijing as it seeks to avoid further scrutiny.
If we apply the RAM model individually to all the countries that voted in favour of China, what do you believe was their own goals and objectives for defeating this motion? Do you genuinely believe that some of them believe that China hasn't committed any human rights abuses against the Uyghurs or Muslims? That isn't really in question because even China knows it is acting in excess and some of their political actions are indeed abusive. But, the Chinese believe that it is necessary and justified to protect Chinese interests. Now that stand is more easy to accept for many non-western states that supported China because they too know that sometimes when states act violently against some group in the national interest, human rights violations do happen. And it is of course, in their best interest not to have this scrutinised by the world.
That's one of looking at it.
Another is perhaps China threatened some of them, and so they again voted to preserve their own economic and political interests over that of issues of Ugyhurs or Muslims that may not have any political impact on their own country.
And so on.