The question of how to clean American diner furniture is actually not one that should cause a great deal of concern - this is restaurant furniture that is designed to look good, yes, but that doesn't come at the expense of practicality, and it's very easy to maintain.
First of all, there are the materials - stainless steel legs for the chair and stool frames, and solid hardwood for the base of the bench - which provide a sturdy and durable skeleton on which the upholstery is then applied.
The upholstery itself is protected by high quality faux leather, and this is both hard wearing and resistant to stains and reasonable levels of dirt.
Remember also that although you might think of American diner furniture as being red and white, it is actually red and cream - and that off-white colour is much easier to keep looking pristine over the long term, without resorting to harsh chemicals and bleaches.
In practice, the best way how to clean American diner furniture depends on the type of dirt you need to clean off of it.
Dry dirt - such as pizza crumbs, if you serve a traditional American menu - can usually just be brushed off. Despite the two different colours, diner furniture typically has quite a sealed upholstery, with the different panels stitched neatly together, so there are fewer nooks and crannies for crumbs to find their way into.
Give special attention to the join between the cushion and the seat back on the bench, as this is one of the few places where it is a little easier for crumbs to hide - they should still be easy to brush away or vacuum out with a narrow nozzle, whichever you find easiest.
The best way how to clean American diner furniture upholstery itself is just the same as you would any other faux leather furniture - so use your preferred leather polish or surface sanitiser, or even just a damp cloth for everyday maintenance.
If in any doubt, colour-test a small area first to make sure, but generally speaking you should find the upholstery is easy to keep looking at its best with even the gentlest of detergents, watered down in the usual way.