Thanks for your help, Myra!
Rendering the entire text as an image is not an option for me, as I lose sharpness and readability.
But the workaround of grouping only the animated text blocks and exporting them with the "render groups as images" setting works.
For the other affected text parts, as you wrote, I deleted the paragraph style overrides and reset them manually, so it works as SVG. So it seems to have been only a problem with certain text styles.
Thanks again and best regards!