"Like a cleric or a druid but not based on religion or inherent spirituality" can mean a lot of things. Do you mean a healer/support class? Or something else?
We've had the Warlord in 4E which filled a similar role without magic. Bards are arcane healers (as a divine soul sorcerers and Celestial Patroned Warlocks (although they have obvious divine touches)).
There is nothing forcing a cleric (or druid) to worship a particular God. They may draw power from the universe as a whole, and their faith might be a respect for the whole universe.
In my primary homebrew, Ao is the first God (yes, the name is stolen), and is essentially the universe. Ao's existence is so foreign to humanoids that it does not translate into him being a being of any type. As such, he is more of an abstract force, but he does have clerics that draw power from him. There are no teachings for Ao, no specific prayers. It is a very abstract faith.
Additionally, druids have absolutely nothing to do with religion in my campaign setting. They can worship a God, just as a fighter can, but their power is derived entirely from the Positive and Negative Energy Planes. Nature magic comes from the core of life and death. As the Feywild and Shadowfell are both transitive planes I connect to these two mysterious planes, the abilities of the druid align well with the underlying premise - it all fits nicely. Technically these planes are also abstract Gods, in the same nature as Ao, so in a sense there is a divine aspect to it, but it is so far removed fromwhat a cleric is that they seem entirely independent of faith.