"fighting them" is a valid phrase in written English.
This phrase can be used when describing a physical altercation or a figurative struggle against an opposing force. For example: "The army's courageous efforts made them unstoppable; they pushed on despite the enemy's relentless barrage, fighting them all the way to victory."
Exact(59)
We have huge battles to fight -- and we're fighting them.
There are good welterweight boxers to fight, and Mayweather the entertainer isn't fighting them.
We are fighting them.
We're going to keep on fighting them.
He recalled fighting them over the years.
Lerner denied the allegations and is still fighting them.
"You'd think I'd be fighting them away with a stick.
Custer appears to have taken little pleasure in fighting them.
Some of the civilians fighting them were also armed.
Or, in any case, fighting them to a draw.
"But the question is, should we be fighting them?
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com