You can be a fan of something and still see flaws in the writing, characterization and continuity.
You can be a fan of something and dislike the writer/s and their writing style/s.
You can be a fan of something and notice and discuss problematic elements of it.
You can be a fan of something and critique and analyze it.
You can be a fan and do none of the above.
Stop judging others for how they choose to enjoy their media or their opinions and beliefs.