genauso=exactly, just the same, just as
Populaeres=popular
Klassisches=classical
Nachdenken-Nachdenkliches (verb. noun)=thoughtfulness, contemplativeness, pondering,reflectiveness etc.
Lustiges=funniness, cheerfullness, drollness, comicality

The nouns sound kind of odd in English.
Thus, I would translate it this way:
Popular material is presented
just the same as classical and contemplative ones--just like/so is funny stuff/comical stuff.
Or:
All materials are presented the same way whether they are popular, classical,
contemplative, or comical.

Thought-provoking makes more sense than contemplative here. And I wouldn't use the word "material" unless the context allows.
Everything is presented in the same way whether classical, thought-provoking or comical.

The exhibits encompass the whole range from trendy to classical themes, from provocative to humorous subjects.

(More contect would probably have been helpful: e.g. what kind of Ausstellung?) :)

It refers to an absence of discrimination between the high- and low-brow, an openness.

It certainly refers to some exhibits, though some more text would have helped.