The prevailing model of physics prior to special and general relativity was Newtonian. Under Newtonian mechanics, there is no theoretical maximum speed. Prior to the 17th century and the work of Ole Rømer, Light was believed to be an instantaneous phenomenon, however it was not until much later, around the turn of the 20th century, that light's speed was known to be invariable. To a scientist in the early 1800's, it would not seem strange to think that light had a finite speed, but that this finite speed was higher or lower depending on the motion of the emitting body.

It's difficult for me to say that there was definitely never a "maximum speed" under any system of physics or philosophy prior to the 20th century, but I have never heard of or encountered one.