Does getting soap in your eye (by mistake) and/or rinsing your eye out with tap water (to clean out the soap or other chemicals) cause a stye?

No: Nothing to do with your stye. Completely coincidental.

Not due to soap: Soap in the eye would not cause a stye. For good health - Have a diet rich in fresh vegetables, fruits, whole grains, milk and milk products, nuts, beans, legumes, lentils and small amounts of lean meats. Avoid saturated fats. Drink enough water daily, so that your urine is mostly colorless. Exercise at least 150 minutes/week and increase the intensity of exercise gradually. Do not use tobacco, alcohol, weed or street drugs in any form. Practice safe sex, if you have sex.

No: Styes are usually blocked glands - i.e. lid problem and so will usually respond to warm/tepid towelette which melts the secretions and gets them draining. If not may need to see doctor for referral for excision Soap into eye tends to affect the cornea and conjunctiva - the lining itself - causing burning sensation and if severe loss of vision. If in doubt see doctor for exam and diagnosis