I would like to say
"It's hard to fight thinking in stereotypes."
Or
"Thinking in stereotypes is bad but hard to fight."
Can I use 戦う to say this or is there a more suitable word? I'm also unsure of how to say "thinking in stereotypes". ステレオタイプで考えるのは戦いにくい？
Using 「戦{たたか}う」 is not totally impossible in that context, but you would need to know that it would sound like a pretty emphatic phrase that implies that your desire/tendency to think in stereotypes is realy strong.
Your sentence at the end, however, would still be incorrect and ungrammatical. 「戦いにくい」 would not make much sense here. (You are trying to translate too literally from the English.)
If you must use 「戦う」, you could say:
「（つい）ステレオタイプで考{かんが}えてしまいそうな自分{じぶん}と戦うのは難{むずか}しい。」
I myself would suggest that you consider using a milder-sounding 「抑{おさ}える」= "to muffle", "to suppress", etc. and say:
「（つい）ステレオタイプで考えてしまいそうな自分を抑えるのは難しい。」
