why did we use が two times in this sentence, and what does the mean of 豊かになること sentences
To comprehend the reason for the double-が, you will need to analyze the sentence grammatically.
What is the grammatical subject of this sentence? It is 「能力のある人や努力した人が豊かになること」. Yes, the subject itself is a mini-sentence that is nominalized by 「こと」.
Since the subject is a nominalized mini-sentence, it just so happens that it contains a が within itself. That is the first が in the whole sentence.
That rather long subject must now take the subject marker, which is the second が. Thus the core structure of this sentence is:
"A が B だろう。" = "A would be B."
A (subject): 能力のある人や努力した人が豊かになること "that those who have abilities or have made efforts become wealthy/successful"
B (predicate): 本当の平等というもの "what should be called 'true equality'"
Hope this helps.