would you say that purposely not hiring people because they are LGBT is not an unjust exercise of power?
Hiring people isn't an act of power. Employment is a contract, a dual-sided agreement. You don't force people to work for you, and you can't control their lives in any way.
Power: possession of control, authority, or influence over others
In a free market, an employer doesn't possess any control over the lives of their workers. Calling their ability to make agreements "power" is a purposefully wrong way to use the word. By the same logic, a criminal using his bodily power to steal a car is "oppressing" the owner. This doesn't make any sense (if you disagree, please explain why it makes sense). Similarly, it doesn't make sense to claim that discrimination in the hiring process equates to oppression. It is still a bad thing, but it is just discrimination, not oppression.
Or realtors doing the same for selling houses, or SOGIECE doctors refusing medicinal service to these people?
I can raise the same objection. These people can't control the lives of people. They are merely refusing to serve a particular group. This is the definition of discrimination, not oppression. For something to be called oppression, it needs to be real power. Real power, as in "being in control of someone else". Only the government and similar institutions have the ability to oppress.
Morality, as a principle, has to be subjective
...
certain axioms that we must accept
You mean that people have a responsibility to follow moral axioms but that any conclusion is necessarily subjective. I see...
In practice, this means that society can interpret the axioms in a subjective manner to create a moral standard, but they cannot change the axioms themselves.
they have to necessarily accept that what they did was wrong
They have to accept that maltreating people is morally wrong. But even today, we lock people up in prisons and kill people for being criminals. Why? Because we have other moral axioms in addition to loads of other factors contributing to moral prioritization. Imagine if humanity in the future reaches a "higher" moral plane where they despise our treatment of criminals, concluding that nobody should be treated badly, even if they do things we today considered immoral. We would call out their judgement as unfair, as they were not considering the other factors contributing to today's moral standard. Would you disagree? Do you think our treatment of dangerous murderers is morally wrong? I don't think so. From our perspective, it is most beneficial for society to imprisson criminals. This principle can be applied to any historical period and its respective moral standard. Therefore, it makes no sense to judge the moral standards of the past. It only makes sense to judge people in the past using THEIR moral standard.
I conclude:
A: Punishing immoral actions is not immoral
P1: One can only judge the actions of a people by their own standard
P2: The moral standard of the past condemned LGBT as immoral
C: People punishing LGBT in the past were not immoral