There is no reconciling these positions. Society is a struggle between them, with one side or the other gaining the upper hand at different times.
It seems you’re suggesting that certain current societal victories (like say Civil Rights) aren’t actually achievements of justice and fairness but merely “one side” and their arbitrary views having the “upper hand” today.
Many philosophers are going to say that’s completely wrong and that we can determine what justice actually is.
What are you talking about? I'm sorry but you don't understand basic Philosophy. Plenty of philosophers give answers. You're saying John Rawls dedicated his life to thinking about justice and came up with no 'answers'? Ridiculous.
John Rawls had some very nice ideas about justice but by no means did he settle the debate. For one thing, he was a utopian, opposed to property rights. That is unrealistic, unless you’re talking about some hypothetical post-human society.
To create any workable theory of justice, I think you should start with the basic assumption that you’re dealing with human beings who naturally incline towards competition and status-seeking. Envisioning a society without some of the traits of human nature is the epitome of Utopianism. You might be able to engineer these traits out of human beings but then you’re dealing with a post-human world.
While there are people who hold extreme positions on redistribution, most people in general actually seem supportive of ameliorating the plight of the poor, and I would say broadly do believe that doing good for many at some expense of the few is justified. Many people even will go to great lengths and do charitable work among other things.
However, cash redistribution which is arguably a very effective way to accomplish the same thing still faces huge opposition. Suddenly otherwise charitable people will start talking about 'welfare' in disparaging tone and so on.
Paradoxically you were more likely to find support among people like Milton Friedman ("the thing poor people need the most is money") who was not exactly known for his left-wing views.
there is something different going on with cash redistribution that is separate from general notions of fairness. My guess is that there is still way too much cultural emphasis placed on the notion of work. People would rather have poor people receive a salary for meaningless menial work rather than just flat out receiving cash assistance.
Of course UBI and helicopter money ruffle feathers. They directly contradict the basic assumptions our political systems are thought to work on.