From the online grumblings of web designers I've read, IE is terrible at a lot of things. And, in general, there are three solutions:
- CSS that adapts to a user's browsers
- Warnings which advise users to switch browsers
- Accept that IE is bad and stop caring
If you're comfortable writing custom CSS, #1 would be best. GitHub's doing #2 right now, and it might be possible to do within a Shiny app. If you can figure out when a session is using IE, you can make a pop-up warning saying things won't look great.
#3 is easiest, but if you expect most users to have IE or are required to cater to IE, then it's a no-go.