General:
* Sensitive topic
* Delicate matter
* Hot button
* Taboo
* Forbidden subject
* Controversial issue
* Painful subject
More informal:
* No-go area
* Off-limits
* Elephant in the room
More specific:
* For personal topics:
* Private matter
* Personal issue
* Difficult conversation
* For political/social topics:
* Polarizing topic
* Divisive issue
* Charged subject
The best synonym will depend on the specific context and the level of formality you want to convey.