That's NOT true as Ellen says. If you don't nurse during mastitis (even if you have a super duper pump) you are putting yourself at much higher risk of getting a breast abscess and needing surgery in the future - no fun.
By the time a mother has a fever the baby has been long exposed to the relevant bacteria/ virus and now needs the relevant antibodies/ antivirals.
Even if the quality/ consistency did alter slightly - that's hardly a reason to stop - and do what? Offer formula? With mastitis sodium levels in the milk rise slightly but it's still good old breastmilk.
Very very few medical conditions where a mother should stop breastfeeding.