I think you might be conflating the Streisand effect with something else?
The Streisand Effect describes the case where a party (business, person, etc) attempts to tell people to ignore or not look at something they disapprove of, which then causes people to go look at that thing. The origin of the term comes from Barbara Streisand filing lawsuits to attempt to suppress photos she didn’t want publicized, which ended up popularizing the photos (because people heard about the lawsuit). For more context: https://en.m.wikipedia.org/wiki/Streisand_effect
I’m thus not sure how it could be immoral, given that the effect is perpetrated by the person who ends up negatively impacted, not by the resulting people who learn about the disputed content.
If you’re referring to the mob mentality that often follows the public becoming aware of something (either via the Streisand effect or otherwise), I agree that the morality of using quantity-of-displeased-humans-on-the-internet as a tool for changing behavior is a dangerous and often misused method.