BhagwadGita is a revered scripture in Hinduism, revered even by atheists like me (wisdom from anywhere is welcome); but I think you know or need to realize that it is basically a Vaishnava scripture with Krishna playing the main role.
Gitas are a genre in Hindu scriptural literature (compendiums of wisdom) with verses compiled and interpolated by many unknown authors over the ages and ascribed to a God or a mythical Sage. Bhagwad Gita is not the only one. There are many other Gitas: Ashtavakra Gita, Avadhuta Gita, Uddhava Gita, Vyadha Gita and Yoga Vasishtha, which is a conversation between Lord Rama and his teacher/family priest, Sage Vasishtha.
Then there are conversations between people, like 'Yaksha Prashna' (dialogue between Yudhishthira and a Yaksha), Yama-Nachiketa Samvada (converation between Nachiketa, a boy who was sacrificed for the crime of asking questions, and Lord of Death, Yama), Yajnavalkya-Maitreyi Samvada (conversation between Sage Yajnavalkya who wanted to become a ascetic and his philosopher wife, Maitreyi). These also fall in the category of Gitas.These were all written after the time of Lord Buddha.
So, as an atheist Hindu, I will accept some verses of BhagawatGita, but will not accept the verses where Lord Krishna claims to be the Supreme God. However, I can accept Lord Krishna if he speaks as a virtual Brahman and not as the Supreme God.
I have no problem if Krishna speaks as Brahman, without being the God, that I am in everything and everything is in me*.
* Note: The Krishna of the theists says something different. He says (to quote Prabhupada) "All beings are in me, but I am not in them." That is 'Dvaita' (duality) and not 'Advaita' (non-duality). Therein lies my difference with BhagawadGita.
"mayā tatam idaṁ sarvaṁ, jagad avyakta-mūrtinā;
mat-sthāni sarva-bhūtāni, na cāhaṁ teṣu avasthitaḥ." BhagawadGita 9.4