When a seed grows big like a banyan tree we never question its intentions why it developed branches when it could grow like a coconut tree straight up only a single stem.
Diversification is part of cosmic life, inherently inbuilt into the system. Of course not in all cases like a coconut tree.
Initially seem tree of Dharma (righteousness). This was the time when not a single religion existed in whole world. Even Lord Krishna had not advent what to say of Mahavira (who followed about thousand years later) or Gautama Buddha who followed about 1077 years later to coming of Lord Krishna. Even Jesus Christ and Prophet Mohammed advent much later!
In the initial stages of life when existed only Dharma advent Lord Krishna an avatar of his era! With coming of Lord Krishna no new following or religion evolved. Even though status of Lord Krishna is much higher than that of man gods like Mahavira, Gautama Buddha even Jesus Christ and Prophet Mohammed but no religion developed after Lord Krishna.
Reason being Lord Krishna represents, was an embodiment of Dharma itself. Prime reason why Lord Krishna is also called Dharmaraja, one who succeeded in re-establishing Dharma (righteousness) defeating evil forces of adharma (lawlessness)! The advent of an avatar gets necessitated when society reaches a point of no return. In Dwapar Yuga came Lord Krishna and to annihilate dark forces of nature of Kali Yuga, mankind awaits advent of Kalki Avatar.
After advent of Lord Krishna the tree of Dharma developed its first branch and manifest Mahavira, the 24th Tirthankara of Jainism. Mahavira did not agree to some principles of life dictated by Lord Krishna in Bhagavad Gita. He developed his own theories different from Mahavira and became the 24th preceptor of Jainism. There was nothing wrong in that. As ordained by God every single human being possessed free will and exercising power of discrimination one could develop a different chain of thought. And this is exactly what Mahavira did.
About 77 years later to coming of Mahavira the tree of Dharma developed another branch and advent Gautama Buddha. The thinking of Gautama Buddha even varied from both Lord Krishna and Mahavira. He developed his own chain of thinking. And the precepts he evolved came to be known as Buddhism. As time passed by the tree of Dharma developed more and more branches and advent Jesus Christ and Prophet Mohammed followed by Adi Shankaracharya and other Hindu sages!
It has rightly been said as many human beings as many different paths to God Almighty can there be. As many human beings as many different chains of thoughts can there be.
Those who did not agree with thinking of Jesus Christ came to be known as Protestants, they protested against the theory propounded by Jesus Christ.
Coming back to the root query, it is not that Gautama Buddha rejected doctrine of Bhagavad Gita but he developed his own style, own chain of thoughts.