Yes you can be intolerant to broccoli or allergic to broccoli.
Intolerance or being allergic to broccoli is rare but does happen to some people just like you can be intolerant or allergic to any other food, drink etc.
Some signs and symptoms of broccoli intolerance are mouth tingling, nausea, wheezing, face or lip swelling, running nose, coughing, sneezing and itching.
If you experience those symptoms after eating broccoli then you could be allergic or intolerant to the broccoli.
However for those not allergic or intolerant to broccoli the broccoli including the broccoli stalk is very healthy and nutritious.
You can eat broccoli stalk.
All parts of the broccoli are edible including the broccoli stalk.
The broccoli stalk is just as nutritious and healthy to eat as the entire broccoli is and broccoli stalks are low in calories and high in fiber.
Broccoli and broccoli stalks are a great healthy food to keep you feeling full and also helps you lose weight.
Broccoli stalks are not only good to eat by themselves or along with the broccoli itself but broccoli stalks are also great for putting in foods and dishes such as in soups, salads or stir-fry them.
I've stirred fried broccoli stalks and it's very delicious.