Whether to add the core of fruits and/or the seeds of a fruit to a green smoothie is a simple matter of taste. The stems of fruits like grapes or apples don’t contain any real nutritional value, so you can discard them.
Seeds can have nutritional benefits but tend to have a bitter flavor; if you aren’t into bitter smoothies, you’re better off leaving out all the seeds and going with a smoothie that tastes good because a good tasting smoothie is one you’ll drink every day.
Honeydew melon and cantaloupe seeds are high in protein and are full of powerful antioxidants along with vitamin E, magnesium, phosphorous, and potassium. Definitely add these seeds to your green smoothie! Watermelon seeds contain zinc, iron, and protein, so including them in your smoothie is a good idea as well.
Citrus seeds such as lemon, lime, and orange are edible, but they tend to be bitter. If you don’t mind or don’t notice the bitter taste, then adding them to your smoothie is fine. Strawberry seeds and blackberry seeds are okay too. Blackberry seeds in particular are rich in protein, carotenoids, and omega-3 fatty acids.
Apple seeds contain amygdalin, a substance that produces cyanide through the process of digestion. This same substance also occurs naturally in apricot, cherry, peach, pear, and plum pits and seeds. Blending up one or two apples plus a pear, seeds and all, isn’t going to do any damage, but you’re still probably better off cutting away the core and throwing out the pits, adding only the fruit to your smoothie.
The avocado seed contains high amounts of potassium and powerful antioxidants; you can blend them, but only if you have a high-power blender such as a Vitamix. Large seeds or pits like avocado are just too big for the small motor in a standard household blender. Avoid mango pits altogether because they haven’t been found to be edible in a raw form.