«Typo3 always replaces the class I selected in the RTE for a table with the class "contenttable". Do you have an idea how to switch that off?»
Assuming that you have installed extension CSS Styled Content (css_styled_content), add the following line in your TS template Setup field:
lib.parseFunc_RTE.externalBlocks.table.stdWrap.HTMLparser.tags.table.fixAttrib.class.list >
The contenttable class will then be added only if no class is specified for the table.