Is money earned from advertising permissible accounts on Instagram lawful or unlawful, given that the account holder often publishes unlawful news about artists?

It is permissible to be compensated for advertisements and to profit from them if the advertised content is permissible and the advertisement does not contain any Shariah-prohibited elements. The fact that the advertised account publishes some forbidden content does not make it impermissible to advertise permissible things for it and receive compensation for that.