Which is a stronger constraint on vehicle appearance: aerodynamic theory or manufacturing? If we gave Henry Ford a peek at our modern cars, would he fail to recognize it as a car? Or would it his reaction be "I really wish I could make cars like that on my assembly lines but the technology I have doesn't support it."
The answer depends on what exactly you mean, and what vehicles we are talking about. So I'll restrict this answer to cars. (Airplanes is a completely different issue, if the Wright brothers had been shown a model of a F-117 and you had told them it was a future airplane they would probably have laughed at you).
The ideas of aerodynamics go back a long way, and race cars quite early used primitive ideas of aerodynamics, like the 1899 land speed record holder La Jaimais Contente. However, the position of the driver outside the body and the exposed chassis likely undid most of the effect of the body. So there was an early understanding that aerodynamics was desirable, but not much knowledge of how to do it well.
And that's one of the reasons early cars wasn't aerodynamic, people simply didn't know how to make them aerodynamic. When in 1914 an aerodynamic prototype was made of an A.L.P.H.A 40/60 the speed increase was 86 mph, compared with 78 mph for the standard model, this not only because of the bad understanding of aerodynamics, but also because the bodywork became much heavier.
In addition to that, the technology to make modern aerodynamic bodies is likely to have been expensive or complicated.
So to answer your questions:
1908 Henry Ford would certainly have recognized that modern cars were cars, and would probably not have said "that car can't possibly work", although I'm sure he would be surprised and astonished by many things.
He would probably have realized that they were more aerodynamic than a T-Ford. He would however likely been very surprised by the aerodynamics. For example, the main aerodynamic trick today is to make cars wedge-shaped. As seen from the cars linked above, the thinking a 100 years ago was that cars needed to be teardrop shaped or oval to be aerodynamic. That a wedge also works is somewhat counter-intuitive.
As a result, he might have actually thought "I wish manufacturing technology meant I could make cars more aerodynamic", while if he was shown a modern car, he might have realized that he actually had the technology.
So why weren't early cars more aerodynamic? Well, here I can only speculate. First of all, a Model T's top speed was 40-45 mph, so the benefit of aerodynamics was limited. Secondly the roads were not good enough to allow that top speed anyway. And thirdly, as seen above, they probably thought aerodynamic cars was harder to make than was the case, and this means they didn't even try. The first company to use wind tunnels to try to make an aerodynamic car was allegedly Chrysler in 1930, which resulted in the 1934 Chrysler Airflow.
And lastly and most importantly, people expected cars to be horseless carriages, and look like carriages and have the same sort of comfort as carriages. That meant cars were tall, with high straight seats. Today when we sit in a car we sit down, and expect to lean back and have our legs forward, and not sit like you sit at a dinner table. If you introduced a car that is styles like a modern car on the market in pre-war US, it probably would have been an utter flop, because people would not know what to make of it, and they would have found it strange and uncomfortable. And indication of this is that the above mentioned Chrysler Airflow that indeed was lower than most cars at that time, also was a commercial flop, although the design was hugely influential.