Why didn't Paramhansa Yogananda prohibit the usage of onion and garlic as in Indian yogic tradition? These are considered tamasic and are strictly prohibited.
You are right, garlic and onions are traditionally banned from the yogic diet. Yogananda however listed them as rajasic (stimulating) not as tamasic (darkening). That is a big difference.
Swami Kriyananda explains in his book Art and Science of Raja Yoga that indeed the yogic diet focuses on harmonious (sattvic) rather than stimulating (rajasic) foods. Sattwic foods keep the nervous system cool, relaxed, and peaceful, which is better for our meditations. Sattvic or elevating foods also make our consciousness more spiritual. Rajasic, meaning heating and stimulating foods, activate and excite our nervous system, which makes it more difficult to be spiritually focused.
However, Yogananda was never a fanatic concerning food. He allowed some rajasic ingredients, also in his ashrams. Why? Swami Kriyananda writes (in the same book): “Yoganandaji fed us onions and garlic in America, as well as eggs. I assume that his reason for doing so was that the Western world demands a certain adaptation of the Eastern teachings. Here, perhaps, some rajasic food is desirable, if only to help us to keep abreast of the currents of consciousness swirling around us.”
Concerning garlic and onion: you may chose for yourself to eat them or not.
In general: Yogananda gave importance to a correct diet (which he termed “right-eatarianism”), but didn’t want people to make a religion out of food. He gave, for example, Kriyananda a five dollar note to go and buy an ice-cream. That too, a very traditional Master wouldn’t have done.
Diet is quite a personal issue, having to do with our body type. Yogananda writes in his Autobiography of a Yogi: “My guru was a vegetarian. Before embracing monkhood, however, he had eaten eggs and fish. His advice to students was to follow any simple diet which proved suited to one’s constitution.”
All the best,