Tried it on a more complex structure — the result is the same — webflow takes only tags but no class names, unfortunately.
I found a pretty good use for such a bug/feature.
A footer code! Which is always needed and is always the same. I just copied footer’s code from the browser’s inspector and pasted it into webflow’s text field.
There are some glitches though, conncted with — I believe — that this is a Text Block, not a DIV. You can’t move nested elements, etc.
And no HREFs! The links are A’s, but have no HREF, you need to write the url manually.
I suggest not abusing this bug though - if it gets fixed in the future you may not be able to edit whatever you pasted into the div, or some other weird stuff may cause your project to break.