Gita acknowledges the right of a person to reject its teachings.
‘..Reflecting on this entire teaching, do as you think fit.’
However, Gita has very low opinion about atheists.
According to them nothing is ultimately real in this world. It is
Godless and without any moral basis. Being born of sex union, what
else but lust can be said to be its cause?
We need to deal with 2 cases, that of immoral atheists and moral atheists.
What happens to immoral atheists?
These vicious men, oppressive, cruel and sinful as they are, - are
always hurled down by Me into demoniac wombs in life after life, in
the transmigratory cycle.
What Gita means is that immoral atheists would remain in Samsara, the cycle of birth and death, since they will not do spiritual practice to purify their hearts and know God and will thus suffer.
Of course there are also atheists who live moral lives. What would happen to them? The answer is that they will also remain trapped in Samsara since God realization is the only way out of Samsara. However, they will most probably have pleasant life since they have lived a moral life.
The only way to end of sorrow is to know God. When men shall roll up
space as if it were a piece of leather, then will there be an end of
sorrow, apart from knowing God.
Svetasvatara Upanishad VI.20
Does Gita discriminate between atheists and believers?
The answer is no. Even believers will remain trapped in Samsara unless they purify their mind.
For the attainment of mental purity, spiritual aspirants (Yogins)
perform action devoid of attachment, with their body, mind, intellect
or even merely with the senses.
Intellectual position irrelevant for moksha
The point is that Gita or Hindu shastra does not say that intellectual belief or disbelief plays any role in the fate of a person. It is only mental purity that determines whether a person will be able to escape the cycle of Samsara. An atheist will remain trapped in Samsara not because of his belief but because of not striving for mental purity. It is his choice. Similarly a believer who does not purify his mind will also remain trapped in Samsara. Again it is his choice. God does not play any role in deciding whether any person remains in Samsara or not.