You are exactly mentioning the problem: Safety systems need a lot of space and add weight. Emission control systems add weight and need space. An updated engine most likely will need it's space as well. Especially modern crash tests wouldn't be possible for cars with old systems. They would fail badly. Some systems can't be added without having to change the way the car looks, for example everything related to protecting pedestrians or smaller cars or injury risks from sharp edges in the interior of the cars.

So you could create something like it, but it wouldn't be a Mustang 68 lookalike, but a 2019 Mustang who wants to be a Mustang 68 lookalike.

It has been tried to design cars which have some resemblance of older cars, think about the VW beetle or the Fiat 500 or anything Mini does. But they are / were new cars which just have some stylistic elements of the old ones.