Word for "influencing or manipulating people without their knowledge"

The term I would use is subliminally, the adverbial form of subliminal

(of a stimulus or mental process) below the threshold of sensation or consciousness; perceived by or affecting someone's mind without their being aware of it.

The classic form of this is subliminal advertisingonce thought to be widespread in movies. In this use, a single frame showing popcorn, inserted at intervals into the movie, was thought to induce a desire for popcorn without the viewer realizing that anything had happened. Other, more sinister,uses have been claimed, up to and including political campaigns.

So, your sentence might become, "Social Media content is drastically and subliminally influencing peoples opinions."

Surreptitiously (ODO)

• Obtained by ‘surreption’, suppression of the truth, or fraudulent misrepresentation;

• Taken, obtained, used, done, etc. by stealth, secretly, or ‘on the sly’; secret and unauthorized; clandestine

So,

"Social Media content is drastically and surreptitiously influencing peoples opinions (without their knowledge)".

"The word gaslighting is used to describe an attempt to destroy another's perception of reality."

And in the play which originated the expression, Gas Light, the gaslighter was a bigamist and jewel thief who manipulated his wife into not obstructing his attempts to recover a score.

It's typically used to describe abusive intentions, but (in my experience) has unfortunately loosened to include other attempts to shift the perceptions of others until they match what the manipulator wants them to believe. Either way, I am completely convinced that the social-media activity which you're asking about is indeed deliberately abusive and I find that "gaslighting" to be a very apropos description of what the perpetrators are doing.

https://en.wikipedia.org/wiki/Gaslighting

You can alternatively use the term brainwashing.

Collins defines brainwash as:

verb, transitive, US;

[T]o indoctrinate so intensively and thoroughly as to effect a radical transformation of beliefs and mental attitudes