1. »Von« + dative case is a substitute for genitive case
Very often it is possible to replace genitive case with »von« + dative case without changing the meaning:
Der Griff des Messers ist schmutzig.
Der Griff von dem Messer ist schmutzig.
Der Sohn meines Bruders ist krank.
Der Sohn von meinem Bruder ist krank.
My observation is: People in the south of German Sprachraum more use the dative version, people in the north more use the genitive case. And if you ask people from different regions, which version is more common, or which has a better style, you will get different answers.
In some Dialekts (mainly in the south) you also have this dative substitute:
Dem Messer sein Griff ist schmutzig.
Meinem Bruder sein Sohn ist krank.
(Very famous quote and title of a series of books by Bastian Sick: »Der Dativ ist dem Genitiv sein Tod«)
But this is not standard German. You might hear it, and if you hear it, you should know, that it is used as replacement for a genitive construction in a dialect that has no genitive case. But you better should not actively use it. (As long as you speak German with any accent nobody will believe that you are a dialect speaker, so better don't do it.)
2. There is no way to build genitive plural with an indefinite article
In German and in English you use definite articles if you are talking about a certain thing. If you talk about just any thing, you use an indefinite article:
Das Kind braucht Hilfe. Ein Kind braucht Hilfe.
The child needs help. A child needs help.
This is also possible in genitive case:
Der Hut des Mannes fliegt durch die Luft. Der Hut eines Mannes fliegt durch die Luft.
The man's hat is flying through the air. A man's hat is flying through the air.
Note that there is also a null article (which means you don't use an article), which often is used together with names, and (in singular) has the meaning of a definite article:
Michael braucht Hilfe.
Michael needs help.
Der Hut Walters fliegt durch die Luft.
Walters hat is flying through the air.
But when it comes to plural, there is a problem with genitive case.
Let's first try nominative case and dative case in plural:
Die Frauen schlafen. Frauen schlafen.
The women are sleeping. Women are sleeping.
Diese Autos gehören den Bauern. Diese Autos gehören Bauern.
This cars belong to the farmers. This cars belong to farmers.
As you can see, the indefinite plural article is a null article. (This is also true in accusative case, just didn't give an example here)
But you can't build a sentence in German, where you use genitive case in plural together with an indefinite article:
Das sind die Autos der Bauern. (singular genitive plural with definite article)
Das sind die Autos Bauern. (wrong! You need something between »Autos« and »Bauern«. The null article, which is the indefinite article for plural in all other cases, doesn't work in genitive case plural)
Das sind die Autos von Bauern. (correct, but no longer genitive case. This here is dative case, and Bauern goes with the null article, which is the indefinite article for plural)
Put 1 and 2 together
So, if you understand both facts, you will see, that, if you want to build a part of speech, that is indefinite, plural and genitive, you just can't do it. You have to use another construction.
One way is not to insist on an indefinite expression:
Das sind die Autos der Bauern.
Die Belange der Minderheiten sind zu schützen.
But if you are not talking about certain minorities, but about any minorities, this is not what you want to say. So you have the substitute genitive case by »von« + dative case, and then you can use the indefinite plural article for dative, which is the null article.
Das sind die Autos von Bauern.
Die Belange von Minderheiten sind zu schützen.
Just to show:
You can also use the dative substitute together with the definite article:
Das sind die Autos von den Bauern.
Die Belange von den Minderheiten sind zu schützen.
But, then you again talk about certain farmers and certain minorities, not about any of them.