If you look at rascism or sexism, as it stood in the 19th century, it was used to exclude certain group of people from their rights. So black people (in the US) could be enslaved, and women couldn't own property and were effectively the property of their husbands. Neither had the right to vote.
This acts as a systemic mechanism to reduce the status of groups (not individuals). Just as stereotyping assigns all members of a certain group with an attribute, these political tools deprived people of their rights based on precieved inherent biological flaws.
But that skips several layers of understanding. First you have to understand status, it is based on respect and trust; if one of your friends is respected and trusted by everyone in the group, they can be understood to have higher status, when they speak others will listen, when a group decision needs to be made they will have more influence (and it is not as simple as that, some people may be trusted on certain subjects and not others).
This comes down to personal experience, you get to know the person, and they earned that trust and respect.
This is a very costly and time-consuming exercise, so we have developed several shortcuts. Money shortcuts trust, when you are paid money, you trust that someone else will accept that money for things you want later; it holds value only because of this social trust, and you are willing to exchange your labour for it because you trust the money even if you didn't trust the employer. Money can thus be used as a substitute for power in some ways.
Respect also has its shortcuts, we can respect position rather than the individual who holds them. Your local school headmaster position is one which is respected. All the other parents sending their kids to the schools respect the position, so you feel you can, without necessarily knowing who the individual in this position is. You take the shortcut to respect by you respect the institution - and that nobody lacking the necessary reapect could hold the position.
So institutional position and money can be shortcuts to high status within a society.
Two useful shortcuts. Rascism in particular is a piece of political technology used as a shortcut to lower the status of entire groups. Again, without the time-consuming effort of getting to know them. The Internment of Japanese-Americans during world war 2 was a clear example of this in action. Japanese-Americans were seen as a potential threat by the high status individuals, so thry were excluded from their rights (to a fair trial) and collectively had their status implicitally reduced.
They were not listened to, or respected.
The more extreme example is the Nazis excluding Jewish and LGBT and disabled people from the right to life.
Rascism is a propoganda tool, to lower the status of groups. Excluding them from their rghts. It can be very effective, because lower the status of one group implicitly increases the status of others. White supremecists like racist ideas because thry are elevated (while doing virtually no work to earn it) to a higher status than non-whites.
Today we see muslims excluded. But also poor people. The assumption being that your worth as a person is determined not by skin colour, gender, or religion, but by your bank balance. This is affording the most respect and influence to those with the most money.
It is a system which says not all humans are equal or deserve equal treatment, but that status buys them rights. And money is the only important consideration when accessing someone's status.
Socialism is the ideal of a classless society. It is one where no group is held above another. Where all people are consider equal, regardless of what job they choose, or where they went to school, or any other consideration. And now i vere into the hypothetical, because there has never been an ideal socialist state. One where money doesn't equal power.
Human nature being what it is, people will seek power and status even without money. For example, in the soviet union, when the currency was restricted in what it *could* buy (whether due to rationing or close markets) workers would do overtime, produce more than their quota and sell the excess privately for gold. The fact that money couldn't be used meant it had lost the trust we place in it, and the workers found an alternative method for accumulating power (in systems with money someone could simply have skimmed some cash off the top).
In an ideal socialist state, people would still strive for status. Like Olympic athletes, they would compete to be the best, strive to earn a reputation, even without money or power resulting from their achievements. Scientist would still compete for prestige, even if they weren't competing for grant money.
Socialism requires not just the elimination of racism and sexism, or ableism and homopobia, or transphobia and misogyny. Socialism requires the elimination of wealth as a source of privilege. It require dismantling power structures which have existed for millenia. And displacing the wealthy and power from their power.
Some of that may seem challenging, other parts impossible. The reason i related the story of Russians circumventing their currency when it's lack of power to purchase goods made it redundant is because whatever solution is proposed, some people will try to find a loophole to privilege themselves.
Today, however, the moves we see in the republican health care bill more away from this ideal. They emphasise the importance of money for determining who should be included or excluded from healthcare. They divide not based on race or sex, but based purely on wealth (though for historic reasons, this will hurt discriminated against groups like women, people of colour, and other minorities which have been discriminated against, more than others).
Health and education can be considered fundamental human rights. Necessary for the 'pursuit of happiness'. Directly affecting the quality of life for all. To those who believe that life is sacred, or that the right to life should be inviolable, i ask simpl this, what is the point in protect the right to life, without also protecting the quality of that life. Would it have been ok for Nazis to have kept all the Jews alive, and only tortured and starved them, while using them as slave labour? Without quality of life, the right to life is rather meaningless. And we must act to protect that.