Does eliminating advantages, differences and competition work to eliminate prejudices (racism, sexism, ageism, etc.)? Why/why not?

If it's possible, it will take a long time. Short No. Long Maybe

Explanation:

I believe it necessarily wouldn't eliminate it all the way. This is due to the fact that we as a society have set certain stereotypes for races, sexes, etc. that would be hard to overcome due to certain peoples mindsets and the way people have been taught. There will always be advantages, differences, and other things that will eventually lead to some sort of prejudice among society.

Such as the biggest thing that will take much effort to eliminate is simply the wealthy people in society. Due to wealthy people in society, “During the last few decades, the economic rules of the game were changed, by wealthy individu­als and corporations... There have also been cycles of great inequality in our country's past. In the 1880s, as the United States went through the industrial revolution, there was grotesque inequality as the richest 1 percent owned an estimated 50 per­cent of all private wealth...Yet today, about one out of five households in the United States has zero or negative wealth. This means they literally have no financial reserves to fall back on in times of trouble or, in fact, they owe more than they own. The percentage of households with zero or negative net worth doubled in the last thirty years, increasing from 9.2% in 1962 to 18.5% in 1995” (pg.171-179). Just with the wealthy people, applying that to your question of course, would be hard. Though looking at it, someone has to own a company, someone has to be at the top, therefore wealthy people will never go away in a sense and that advantage and difference can't be overcome.

Now if you simply want to look at advantages and differences between sexism, that's a whole different story. Us as a society, as I said, have set these certain stereotypes throughout the years that would be hard to overcome, such as Patriarchy and Toxic Masculinity.  “Patriarchy...Is the biggest hinderance to our success. We all had these great dreams and stuff when we were little kids, but at some point it was more important for us to be tough. It was more important to us to not back down...To buy into toxic masculinity...Put the patriarchal expectations that the world had on us before our own goals” (30:56-31:22). This can apply to racism as well. People have been taught to handle their own and if it's a male, handle stuff for women too. It is continuing to be taught and kids learn it and grow up with these ideas.

If we want to eliminate certain advantages, differences, and such, it has to start from the base. That being the children. We have to teach kids the "right" morals and values so that they can apply that to their future and to the next generations.

In theory it would seem that eliminating advantages and differences between such would eliminate prejudice but I simply don't see that happening. If it does, it will take a while

(Sorry for this really long answer, I wanted to put it more but I didn't know if I should...Even more I don't even know if this will help you. Atleast I tried lol)