So in my story there is only one major advanced city left in the world, and it is incredibly diverse. I would imagine that over time (it has existed for around 800 years) there would be considerable miscegenation but also probably many different looking people. If people in that city were taught to accept all genders, sexualities, and ethnicities, etc. could there be no more discrimination? (I mean discrimination over things people cannot control) Or will there always be people who believe they are superior to others? Sorry if this is too broad; feel free to edit it and make it more focused.
Equality is a pendulum, not a plumb bob
The short answer to your question is no, there can never be an absence of discrimination because being equal is not being the same. As a result, what makes us 'equal' is an acceptance of difference and ensuring that each of us is treated in a way that doesn't advantage or disadvantage us in any way that creates an unfair advantage or disadvantage - and therein lies the rub.
Kurt Vonnegut wrote an interesting satirical short story about this very problem called Harrison Bergeron in which an equality commission takes the need for equality to an extreme. It's actually an interesting read but the key point of it is that the only way you can eliminate inequality is by making everyone the same and that is never going to happen. Just as an example, let's take a couple of examples and explore them from a needs perspective.
Gay people (for example) need the right to marry their life partners and share the same benefits of that commitment as hetrosexuals. That seems obvious right? But there is an argument amongst hetrosexuals that the reason THEY get married is to have and raise the next generation by having kids - they state that the benefits they get from marriage is really a set of benefits designed to support families rather than couples.
That some hetrosexual couples marry but don't have kids, and some gay couples marry and adopt kids or have surrogate kids only serves to muddy this argument even further.
The simplest answer is that both arguments are correct and need to be balanced through a careful set of policies that don't punish couples for having kids, and don't punish couples for NOT having kids, regardless of orientation. The childless couples will always argue that they are being discriminated against when people with kids get first preference to take holidays at Christmas and get child bonuses, etc. Couples with kids will always argue they are being discriminated against when they DON'T get those things.
Ultimately the balance is going to be set by a simple supply and demand curve - too many kids being born? We dial back all the family incentives. Not enough? We dial them up.
The trouble is, every time we change that someone loses out, and it's easier to just think that it's someone else's fault. That's what causes discrimination in the first place - perceived inequality.
On top of this, some 'rights' that people have or need are going to be at odds from the rights of others. We say that everyone has a right to free speech and to articulate their opinions, but we actively stop 'homophobes' and others from expressing theirs. Whether we find it tasteful or not, we do tend to limit the rights of those we feel are arguing against our inclusive society. How many people abhor the burning of books that took place during Nazi Germany, but would happily burn a copy of Mein Kamph if it came to hand?
I'm not arguing a position here mind you - what I'm trying to highlight is that equality is a subjective assessment and people can only be equal from our own point of view and our own prejudices, whether they are justified or not. Because equality is subjective, it acts as a pendulum. Right now, the pendulum has swung to the side of inclusiveness and giving extra rights and benefits to those we consider disadvantaged. Eventually, that will swing back and the rights and freedoms of the individual will come back into fashion, regardless of what that person feels or thinks.
The only way to eliminate prejudice in our world is to move to objective equality rather than subjective equality, and that means becoming the same as everyone else. That is not a world I care to live in and I suspect I'm not alone in that regard.
Equality is unlikely as long as the beings are human as we know them. Realistic Conflict Theory suggests that people will find some way to create in-groups and outgroups, fragmenting society.
If this city is not the only city left in the world, there will always be conflict between those inside and those outside. If it is the only city left in the world, there needs to be some constant, ever-present hostile force to unite the inhabitants against or they will find some way to group together attack one another.
...Then again, it's up to you as the creator of the world how to define 'equality' and how to structure the society.