No, as a practical news matter, there is the audience, and the percentage of the audience that the outlet can attract. Fox, like it or not and I don't particularly, attracts a larger share of the market than other news outlets. Your statement reminds me of a quote from Stan Freberg when I saw him speak many years ago. He had been offered Jack Benny's time slot on NBC when Benny elected to leave television (Freberg had inherited Benny's slot on radio when Benny went into television). Freberg made comedy records, and they had mock, very funny, advertisments on them. An NBC executive said he wouldn't be able to do comedy ads on television -- audiences wouldn't accept them. "But, I sold six million records with them." "He looked at me with great seriousness and set, "those were regular buyers, they were record buyers." So I got in my brand new 1957 Trojan Horse and started an advertising company."
There are not "Fox News Audience" and "other news audience." There's an audience. Fox is an example of niche marketing -- that audience wasn't being served by the major news outlets -- and Fox took advantage of that. Where you should, if you're a liberal, be concerned is at how large the niche turned out to be.