At the turn of a century, a lot of hair care products were available, most of hair styling was done with Pomade, which was produced by large manufacturers, like Henkel Group in Duesseldorf, which was selling all over Germany in that time, or many small producers. https://books.google.cz/books?id=9Z6vCGbf66YC&pg=PA205&lpg=PA205&dq=german+hair+pomade&source=bl&ots=YM46EZk6q8&sig=ACfU3U1R2CxjxqGYGH8-gGq78G03-BAuoA&hl=en&sa=X&ved=2ahUKEwjUg_L4w_biAhVIIVAKHS-aCE0Q6AEwIHoECGEQAQ#v=onepage&q=german%20hair%20pomade&f=false

Many newspapers and magazines had pages of commercials for men hair care products, like pomade, wax, which was mainly for moustache and various more or less fraudulent products for hair coloring and even hair growing. It is necessary to note that chemical hair coloring existed, but was a complicated and risky process so was done safely just by some professionals. Temporary coloring with pigment in pomade was popular, but the effect was obviously different.

A hair loss was a much larger issue, obviously neither they had nor we have any cure for it, thus some men wore wiglets and some, especially older gentlemen, just shaved their heads entirely. Of course due to types of shaving tools, this became much more prevalent with the widespread usage of safety razors by the turn of century.

With all this said, a well groomed hair was important, having kept hair, beard, nails etc. was sign of a proper gentleman. Of course there were many types of styles and some people didn't care about fashionable look so much, or decided not to follow the trend of kept hair out of principle. The example would be Pierre Curie https://en.wikipedia.org/wiki/Pierre_Curie#/media/File:Pierre_Curie_et_Marie_Sklodowska_Curie_1895.jpg who, as his wife, didn't follow fashion trends but kept a clean and non-excentric look.

August Bebel had a hairstyle that not unusual in his time, it wouldn't be considered overly fancy and probably nobody would find it worth objecting to.