Well I suppose bigotry is more so intolerance of another's opinion or beliefs rather than the person themselves so would you prefer I call her prejudiced or racist?
https://www.merriam-webster.com/dictionary/racism
https://www.merriam-webster.com/dictionary/prejudice
If you have an argument for why these definitions don't apply then let me know. I suppose you can argue that Inhumans aren't a separate race but the humans that mistreat them certainly do so in part because they view them as not human and a threat to humanity. But May's dislike for them is unfair and irrational because she is blaming an entire group for something they didn't do. So that by definition is prejudiced or racist.
At the end of the day, this is just fiction so it really doesn't matter. People can love characters with disagreeable traits because it's a story. However, trying to pretend May is not being prejudiced or racist because you like her is as odd as trying to pretend Hannibal Lecter is not a murderer because you like his character. Their actions speak for themselves. We as readers of a fictional story are free to like a character even if their behavior would be inappropriate or wrong in the real world. What May did would be 100% wrong and prejudiced in the real world. I mean Hydra is a Nazi organization so acting like it's members couldn't possibly be racist or prejudiced is just odd.