1 Correct answer
In my experience, it's overrides. Try this on one table:
- Save the file
- Select the entire table and remove all the overrides:
- Alt/Opt click on [Basic Table] in the Table Styles panel
- Alt/Opt click on [None] in Cell Styles panel
- Alt/Opt click on [Basic Paragraph] in the Paragraphs Styles panel
- Optionally, Alt/Opt click on [None] in the Character Styles panel
- Then try assigning the table style
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uff...just read through it...that sounds really frustrating. 
Thank you anyways winterm​!
Great news, Paul!
Here's one more tip—when I'm in a table-intensive workflow, I have a workspace set up to make that sequence quick and easy. I call it Table Focus, and it puts all those panels front and center. The feature you are using is an important one for table-intensive documents. When set up correctly, you can format an entire table with one click on the table style (because of the nesting potential—table styles calling in cell styles, cell styles calling in para styles, paras styles calling in GREP and character styles.) In long doc layout, this is the difference between having evenings and weekends free, or not! 
My tables come in from Word, with overrides, which is how I know how to take them off!
Can you show the General view of your Table Styles and Cell Styles panels? Use the outlined button in the chat toolbar.
I hope this is what you are asking for?
And that it helps, even though it is german :/...
But in any case, i did set it up, exactly like you showed in your screenshot.
Table style panel at the bottom - then cell styles, character styles and paragraph styles.
I've never used that plug-in, but I do use this technique successfully, and have for years. Not saying it not worth looking at, of course, just that I haven't yet had a need to look elsewhere. (And that's why I'm not walking away in defeat, quite yet!)
So Paul: that screen shot looks perfect. May I see the general settings of Kopfzeile feat & zentriert? For example:
And so as not to waste your time, did you see the technique in the post for importing unformatted tables? (Link above)
Hi Barb,
Yes i did see the technique and already tried (even though i'm trying to avoid importing the unformatted text). Surprisingly, the same problem occurs!
Attached is the requested Screenshot:
(Just in case it is important: I'm workind in a book (just as learned yesterday ) with several documents.)
Already thank you in advance and for the help here!
Barb, i might have just found the issue!
After i selected the entire table, i right clicked onto it and therewith opened the popup menu. There i opened the table option and clicked on "set up table". (I'm just assuming the menu translations here... might actually be called different)
In the Panel "Table Options" that pops up, i noticed that even though, the right table style is selected and all the settings are correct, it doesn't show that it contains a Header Row (see Screenshot). This even is the case, if i manually select the first row and apply the Header Row cell style onto it!
Therefore it obviously doesn't apply the table style correctly...
Seems like a bug to me...
Or do you reckon there to be a user mistake anywhere?
Anyway, so my approach now is to do everything as already talked about,
than in addition manually adjust the Header Row Setting for each table, than copy and paste the contents of the "old" first Row, into this new Header Row. (It unfortunately doesn't overwrite the "old" header Row, but instead adds a new header Row)
AHA! InDesign can't assign the heading row style unless you have first designated it as an official heading row, either in Word prior to export or by highlighting and right+clicking the row(s) in InDesign. was that the issue?
In both screen shots, the first row is highlighted, and I right+clicked over it.
In this shot, because the first row is already a heading row, this one shows Convert to Body Rows.
In this one, the top row is a body row (note how it lost its cell and ¶ formatting), so the same command reads Convert to Header Rows. Once I re-convert it to a heading row it picks up the cell and ¶ formatting as in the shot above.
More on the topic:
https://www.rockymountaintraining.com/adobe-indesign-header-rows/
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