This explanation does not involve formal grammar, but the practical usage of language to convey ideas using different media.
The source of the complexity is the difficulty of adding punctuation in purely spoken words vs visually aided/written words.
I am going to slightly digress and talk about the "..." around influencer first, and then get back to the practical reason for using the "it/that" construct in your sentence.
When you would speak the original sentence, you could use air-quotes around "influencer", to convey the point to someone who could see you. Or, since it's written down, the quotes are there for the reader to identify the word influencer as a misnomer within the context of the phrase.
However, if you were saying the same sentence over a non-visual medium (say a telephone conversation) you would have to either say
quote, influencer, endquote
or more formally you would have to add the adjvective so-called to get the sentiment of the phrase across:
If it is public knowledge that anyone can purchase followers and
likes, then why does a so-called1 influencer hold weight?
1Notice that the use of so-called removes the need for quotes around the word influencer, and conveys the sentiment of the word influencer being a misnomer.
Now, to the original question. We can rewrite the original phrase as follows and do the reverse process:
If "anyone can purchase followers and likes" is public knowledge, then why does an "influencer" hold weight?
While influencer is a single word, and one could possibly get away with not having quotes or the adjective so-called added to it, the phrase "anyone can purchase followers and likes" is a long phrase and one needs a way to mark the compound phrase as the subject of "if". Here is where the practical use of "it/that" comes in.
it becomes the phrase holder, and that allows the compound phrase to be marked until a pause and "then" is encountered.