What religion is Indiana Jones

His father is Scottish, so probably Presbyterian.

I would argue he has a Christian background but is non practicing. Considering he studies ancient cultures and their beliefs, he might keep his beliefs in his back pocket, so to speak. His adventures reveal all sorts of magic and miracles but he keeps an open mind regardless. There never is a moment in any of the films where he declares himself a true believer, despite what Mola Ram claims, though he does look incredulous when the stones light up.

His father seems to be a strongly religious Christian, obsessing with a Christian artifact and slapping him for saying Jesus name in vain. Indiana probably knew the entire Bible due to that.

Indy is more of an agnostic, and it doesn't seem that the events in Raiders convinced him into becoming religious (he called the gospels a bedtime story in Crusade when meeting with Donovan). Neither did they in Temple of Doom, as it took place before Raiders and Indy is clearly a skeptic when meeting with the army agents in the beginning of the latter.

I don't think he is a religious man

Despite the actor Sean Connery being the worldwide symbol of Scotland, his character is named Henry Jones. Jones is traditionally a Welsh name, that has also been common in England for centuries. Hence, statistically speaking, Henry Jones Sr. was probably a member of the Anglican Church (Church of England) before emigrating to the US. In the USA, the Episcopal church is equivalent to the Church of England.
Indy also has a lucky charm in the Last Crusade (a lighter with a four leaf clover on it). Could this signify some Irish heritage (perhaps from his mother) as well, or just be "lucky" because four leaf covers are considered lucky?
Could Henry Jones Sr., despite his accent, be from Northern Ireland, and hence he Catholic or Protestant (Presbyterian, Anglican or Methodist)?
Who knows?

Perhaps non denominational Christian. He’s clearly witnessed evidence of God in his experiences. He was raised with Christianity. The blaspheme line.

I'd say he's someone who was raised as a Christian but is not necessarily a Born-Again Believer or someone who professes his faith.

I would say Episcopal or Anglican since he seems to come from a Christian background but doesn’t seem to have any allegiance to The Vatican (i.e. Catholic) but has a deeper understanding of Christianity and openness to other religions than most Protestant denominations (i.e. Baptist).