What if a particular candidate organised it and used it for her own purposes?
Let me say first that I am not a lawyer. So take the following information with that caveat.
I don’t think there would be any prohibition on a politician being a founder of a 501(c)(3). The test is in the purpose and activities.
If Media Matters is directly promoting Hillary’s candidacy that would be a problem. They can’t endorse specific candidates.
If Media Matters simply does things that are advantageous to liberals, well, the country is full of c(3) groups like that. They are even permitted to do a fair amount of lobbying since the law was changed a few decades ago.
The IRS is not particularly interested in violations by c(3) groups. There’s no money in revoking a c(3) and forcing the organization to become a c(4), which is also a nonprofit, just one that can’t take tax-deductible contributions.