Can the 'Zutritt' in the following sentence be replaced by 'Eintritt'?
Für Jugendliche unter 18 Jahren ist der Zutritt verboten.
What is the difference between the two words?
By collocation, Zutritt is almost always used to express prohibitions (forbidden for minors, forbidden without a ticket, forbidden to the general public altogether), while Eintritt is usually to do with the entrance fee:
Eintritt frei
Eintritt 3,50
vs.
Zutritt verboten
Zutritt nur für Angehörige
Yes, in this case the two words mean the same and can be exchanged in the sentence.
The two words are very similar, although Zutritt is commonly used for areas, rooms and buildings. Eintritt can also mean access to an event like a concert.
The action of moving into an defined area
Literally it is in-going or going into.
You use this noun for entering a defined area for which you most often need a ticket, and where you will attend a performance or presentation.
If you go to an exhibition, a concert, a performance or to the movies, you need to show a valid ticket, and passing through the ticket-check is Eintritt. It is an action, it is not a right.
Some events are free, than there is often a sign saying:
Eintritt frei
freier Eintritt
This just means, that you don't have to pay. This does not mean, that you are allowed to attend the show. But if you are allowed, you don't have to pay.
The right to enter a defined area
Literally it is to-going or going to with the connotation of move close to something.
This is the right to enter a defined and restricted area. Eintritt is not a right, it is an action. But Zutritt is a right that one might have or not. You can be located miles away from that area, maybe you even don't want to go there, but still you can tell if you have Zutritt to that area or not.
In public buildings, you sometimes find closes doors with this sign:
Zutritt nur für Mitarbeiter
(access only for employees)
This means, that only a well-defined group of people,has the right to pass through this door. You don't need a ticket, and there is no event going on behind that door.
At some bars, sex-shops, adult cinemas and similar places you will find this:
Zutritt ab 18 Jahren
This means, that only people being 18+ are allowed to enter.