doctors are trained monkeys. they can only tell you what they were taught. and what they were taught is meat = bad, and they were taught that because calorie for calorie meat has 10X more carbon footprint than plant food ( plus factory farming is unethical ).
also they can't tell you that you're fat because they don't want to offend you, and also if you lose weight they will lose a customer.
even if protein can trigger a gout attack ultimately when you die it will be from obesity and diabetes and not from Gout.
Gout is your wake up call that tells you that you have bigger problems ( like heart attack and stroke ) coming down the line. Your response should be to lose weight, not to cut out protein.
Cutting out protein of course is actually likely to make you gain weight because protein is more satiating than carbs.