First, Hungary already has fast-food restaurants, including McDonalds, Wendy's (since closed due to poor earnings), KFC, and others.
Second, in determining whether or not the Hungarian government should allow fast-food restaurants to operate within its borders, it is important to consider whether Hungary has the legal authority to prevent such businesses from operating there.
Hungary, as are most countries, is a member of the World Trade Organization (WTO). As a member of the WTO, Hungary really doesn't have a choice other than to allow foreign service industries, including food industries from operating there as long as those industries comply with Hungary's, or any other country's, health and safety regulations. Countries hoping to protect their own companies from foreign competition sometimes try to argue that the foreign product does meet acceptable standards, but those arguments are almost always protectionist in nature and failure when brought before the WTO's dispute resolution commission.
This is an interesting and more complex question than it might initially appear.
On the one hand, governments want to protect their citizens. For this reason, they might want to limit things that might hurt them in the long-run. Fast food, in particular, can be harmful. So, the government may want to limit them.
On the other hand, to promote freedom, governments should allow all restaurants to be come into any region. If a government takes a stand, then the question is where the line is. Consistency will be difficult.
In short, yes food restaurants should be allowed in Hungary.