Just yesterday, lazily following the political developments in my country (Ukraine) where a lot of political "innovations", both home-grown and imported, are constantly being tested, I saw a similar phenomenon being called
Yes, that plain and simple.
All the suggestions made so far apply to situations that differ in important aspects from what you want to say.
A "false flag operation" is when a group of soldiers (or special forces operatives) of country A perpetrate a violent act making it look like they were in fact soldiers/operatives of country B. It has never (to my knowledge) been used for the situation that you are describing, which is a political trick restricted to civilian life. A classic example of a false flag operation is one that gave the Soviet Union a pretext to attack Finland in 1939, when "unknown operatives" shelled a Soviet border guard post, and this act was pinned on Finns (giving the Soviet Union the pretext to attack Finland), when in fact it was perpetrated by Soviet operatives.
"Th fifth Column" is a term amply present in our political discourse when discussing who is a "useful idiot" who, by his/her/their actions, benefits Russian interests, but again this is not used in discussions that do not involve an external enemy. The "fifth column" may not even exist—it might be an imaginary group of people that is accused of working for a different, purportedly hostile, country. E. g., this article from The New Yorker describes how President Putin of Russia sees people who are dissatisfied with his rule as people who try to sow discord and are thus working for the purportedly hostile West.
"Infiltrators" join a certain group—they don't set up a rival group that mimics someone.
People who pretend to be activists (of whatever movement) are just that — fake activists.