When I play a cleric it is usually a dip on another class and I make it a point to talk to my DM about my lukewarm relationship with my God.I voted cleric.
I can have fun with any class, but I have had too many DM's forcing too much because deity.
One of the reasons I like bards do much is they make a suitable alternative support class without that baggage.
The thing that gets me is D&D fiction is full of clerics that have strained relations with their gods but still get spells. Erivis Cale for example is a cleric of Mask and hates Mask. The Drizzt novels are full of clerics of Lolth that don't worship Lolth but still get spells.
That is probably easier to do storywise with a chaotic god then a lawful one -
DM: "Your God won't grant you spells if you don't worship him"
PC: "Sure he will, its chaos duh, I just go with the flow! The idea of rigid rules for worship is patently not chaotic. Us mortals are too simple minded to understand his nebulous and often random machinations anyway"