Is it considered bad style if I have a section with multiple subsections and start my text only in the subsection (no text below the section heading)?
1.1 First subsection
This is where the text starts …
1.2 Next subsection
This is where the text goes on …
I think there is no black and white answer here. I think in books it is uncommon to have no text below chapters and start directly with sections/subsections. Typically you will find this:
1. Book chapter
Here goes some introductory text. [...]
This is a section blabla [...]
More text here
I believe a thesis should roughly keep to that structure, too. While I initially preferred to start with the text in the hierarchically lowest section, I became accustomed with the above layout and prefer it over my old habit now.
Regarding articles and similar publications you should keep to the journal’s style guide, which usually prescribes the layout very strictly.
TL;DR: I don’t think it is considered bad style, it depends on the type of text and the place you publish it.