Ideally: No.

But i live in a materialistic society where status is expressed trough expensive houses/cars/brands and products.
If you buy a expensive gift (for a living person), you show to them that you are willing to go to great lengths to make them happy.

This is the societal norm in (probably) all western countries. And therefore, making a extravagant bureal for a horrific person implies approval for them and their actions.

So if you are not a materialistic person you can give a small burial to a person without disrespecting them, but there will definitely be some people that will then assume that you did not like that person. They will simply assume it without proof, as it is a custom, unless they know that you are a anti-materialistic person.

Should they live in the shame and horror of this person that they probably attempted to curb at some point.

No. Those relatives that have not enabled or supported a monsters actions are of course completely innocent.
And if they want, they can of course mourn the loss of the ability to ever have a nice conversation with that person again.
But a burial is not like mourning in your bed, crying yourself to sleep. There you can accept that you are sad about the loss, even tough the world is a better place without that person.

A bureal however is a public performance that, as you say, is for the living. Not for the dead. It is not useful for mourning, but a ritual to pay the last respects to the deceased person. Not only for their good side, but also for their evil side. And the bigger the burial, the greater the (implied) respect. This holds true in any western/materialistic society, and was practiced in ancient times, where pyramids were built to honor kings, and a bigger pyramid implied a better king.

Therefore holding a large burial for a horrific person signals to the living that you not only miss that person as a friend, but also support their actions and choices in life.

So is it fair to the family not to mourn?

How many families of Holocaust victims were given the privilege and closure of mourning and burying their loves ones?

I agree that no person is at fault for the actions of their family or their ancestors, but, their family's actions do no negate the consequences of those actions. Seeing what people like Hitler, Stalin, and Mussolini did to their own people, nevermind what they did to those of other countries... Do their families have more right to mourn their loss than the people do who suffered at their authoritarian hands?

I would argue no, because life isn't fair, but also because the amount of suffering enacted should not be met with honor or remembrance or respect. The family of authoritarians can mourn in their heads, if they do choose, but I would argue they should choose not to. There's no "separating the art from the artist" when it comes to authoritarian genociders. Mourning their life isn't just mourning the loss of them, but the loss of everything they did in their life as well.

If you've lived the kind of life where people are debating the morality around whether or not you deserve a funeral, I'd say you don't deserve one.