I used to be a research microbiologist but I must admit to being confused by your question. In my understanding General Microbiology is not a sub-discipline of Microbiology; now the two terms are close to being synonyms. For Example the Society of General Microbiology used to publish its journal under the name of “Journal of General Microbiology”, but (mostly for “image” reasons) moved the name to “Microbiology” in 1994. The society retained the “general” in its name as there is no real difference. The American Society of Microbiology has a similar scope but with no “general” in sight!
However in the 19th century things were a bit different, and Microbiology was sometimes used in less wide terms to refer to those working in clinical or public health related subjects. the “general” being added to make it clear that studies covered all types of micro-organisms and environmental, agricultural etc. fields.
Kluyver was more regarded as a biochemist, though he was professor of Microbiology and studied microbes extensively.
Perhaps you could tell us where you saw this about Kluyver? It might help to understand the background to your question.