Campaigners against inequality (who are xampaigners for economic and social justice by and large) do not campaign to make every one "equal", but to make the spread smaller and the lives of those with the least less bleak.
I live in New Zealand which is a modern industrialised democracy and is quite wealthy. We have large sections of our population that are malnourished, inadequately housed, poorly educated and cut off from main stream society. The proportion of our population suffering so was much less in the years between the depression and the 1980s, during which a conscious effort was made by the state to maintain a high wage full employment economy.
The policies that worked then will not work now, but what we have is not working and is generating large costs and inefficiencies.
So it is irrelevant that "inequality stems from the fact that people aren't equal in their strengths and weaknesses". The conditions of the weakest and the degree to which the strongest can corral the resources is what counts
W