A few more details emerge: she was also a vocal advocate for the NRA, and failed to disclose that in her article. She was suspended for failing to disclose the conflict of interest. Absent some strong evidence showing that reason was merely pretextual, she probably doesn't have a serious case for discrimination.
So being an advocate for something is a de-facto conflict of interest? She has made no attempt to hide that she is conservative so I am not sure what conflict is here. By that reasoning no journalist who votes or has any party affiliation could write about politics in America. Unless she has hidden being in the pay of the NRA, or having some close link - like a close relative or friend being an NRA officer, for example - there is no apparent conflict of interest.