Can I remove the "pronoun" field from Contacts?

You cannot. You can offer Apple your opinion in the link below. But with so many people using that field, I doubt they will remove it. Your best option is to simply not use it.

Product Feedback - Apple

You can’t delete the field. You are not required to use it, just like you are not required to use any of the other fields available for contacts.

Select Edit for that contact and then tap on the iPhone and change it to what you prefer.