The phrase "divisive issue" refers to a topic or problem that strongly splits people into opposing sides because they have different opinions or beliefs about it. It creates arguments or disagreements among people. Full definition
It has set the tone for the peaceful resolution of some of the most divisive issues in any society. (slaw.ca)
Besides being illegal, it is also one of the most divisive issues of our time, when one religion attempts to force a belief system on others who have a differing view. (religion.blogs.cnn.com)
It's a deeply divisive issue within the charter sector. (educationnext.org)