If Durmstrang Institute doesn't accept Muggle-born students, where are Muggle-born wizards/witches from the area supposed to study then? Do they don't go to school at all and don't learn magic?
The area of Durmstrang is Bulgaria. I expect every country has a magical school because Quidditch World Cup is played between countries and not between schools and those players need to learn playing somewhere.
So they either go to one of the neighbour Balkan countries, (transportation is not a big problem for wizards) , or Bulgaria has a secondary school that accepts muggle-borns.
I think the second one makes more sense.