In my opinion most forms of atheism and agnosticism are incompatible with Buddhism.
In Buddhism the supreme beings are Buddhas.
The Buddha had much more of an issue with atheists and skeptics of the time than Theists and believers of the time.
Wrong views, highlighted in many suttas seem to closely resemble the views of most atheists:
He has wrong view, is warped in the way he sees things: 'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.' - Cunda Kammaraputta Sutta, (repeated in many suttas that this is a wrong view)
"Sariputta, when I know and see thus, should anyone say of me: 'The
recluse Gotama does not have any superhuman states, any distinction in
knowledge and vision worthy of the noble ones. The recluse Gotama
teaches a Dhamma (merely) hammered out by reasoning, following his own
line of inquiry as it occurs to him' — unless he abandons that
assertion and that state of mind and relinquishes that view, then as
(surely as if he had been) carried off and put there he will wind up
in hell." - Maha-sihanada Sutta
Secularism Buddhism would be viewed as a wrong view.
In the Payasi Sutta, an arahant disciple Kumara debated with someone who has views resembling most modern day atheists:
Once everyone was seated, Prince Payasi said, "Reverend Kumara, I
maintain that kamma does not have effects. I believe that there is no
life after death, no world beyond our own. I think that angels and
demons are things from a child’s dream." - Payasi Sutta
Kumara came up with all types of arguments against the atheist Prince Payasi.
The view that there is no afterlife is opposed in Buddhism numerous times, including in the Brahmajala Sutta:
Wrong view 51: "Here a certain ascetic or Brahmin declares and holds the view: ‘Since this self is material, composed of the four great elements, the product of mother and father, at the breaking up of the body is annihilated and perishes, and does not exist after death. This is the way in which this self is annihilated.’ That is how some proclaim the annihilation, destruction and non-existence of beings." - Brahmajala Sutta
So based on my research Theistic beliefs are more compatible with Buddhism. In Buddhism some Theistic beliefs are viewed as slightly wrong, but nearly as wrong as atheistic and materialistic beliefs.
A lot of people often cite the Kalama Sutta but this is taken out of context as the Kalamas were non-Buddhists and The Buddha was addressing non-Buddhists, when The Buddha spoke to his own disciples he encouraged faith and right views.
Some believe that "Secular Buddhism" and other forms of Buddhism match into the prediction in the Ani Sutta:
"In the same way, in the course of the future there will be monks who
won't listen when discourses that are words of the Tathagata — deep,
deep in their meaning, transcendent, connected with emptiness — are
being recited. They won't lend ear, won't set their hearts on knowing
them, won't regard these teachings as worth grasping or mastering.
But they will listen when discourses that are literary works — the
works of poets, elegant in sound, elegant in rhetoric, the work of
outsiders, words of disciples — are recited. They will lend ear and
set their hearts on knowing them. They will regard these teachings as
worth grasping & mastering.
In this way the disappearance of the discourses that are words of the
Tathagata — deep, deep in their meaning, transcendent, connected with
emptiness — will come about." - Ani Sutta
Thus we see people out to replace Buddhism with a flowery attractive elegant words rather than the truth.