This is now fixed. I outlined some of the basic challenges and fixes in this answer. The short version is this is a byproduct of us having two different markdown engines: one on the client for live preview updates (markdown-it) and one on the server for final rendering (markdig). And the result of them having different implementations, as seen in Babelmark.
We've added a plugin to the client side implementation that should prevent md tables from rendering as tables when there is any text immediately before or after the table so that it's consistent with the server side processing.
Here's an example table you can try for yourself with leading text before the table:
Filled Row Before Table
| simple table |
| ------------ |
| goes here |
And here's the result, wherein the client side preview will not render the table, which is consistent with how the post will be handled on the server side as well:
