Maybe it's not possible for all character pairs, but we could have a font-face with plenty of possible pairs and render them as ligatures.
AD -> render an A that looks like a D when viewed upside down
DA -> render the same character in the other orientation
Then to use the font you need to carefully construct palindromes out of the supported pairs. Of course copy-pasting this would be a pita, accessibility would be non-existent, but could be fun for print and such.
That probably exists somewhere as software, but probably not as ligatures in a font. That sounds cool.
Would definitely be limiting on which words you could make a readable ambigram though, because many ambigrams rely on letters that aren't one-to-one mappings (one letter becomes two, or letters between letters, etc.)
Fonts can be complicated. Using nonsense like [1] (specifically contextual alternates), you could have the glyph for the first letter of a word depend on the last letter. I don't think you could get that to work for all letters in an arbitrary length word, but making a font that works for all words shorter than say 20 characters should be doable.
[1] https://blog.glyphdrawing.club/font-with-built-in-syntax-hig...
This is a cool idea!