From the Cleric's Luck Domain:
Good Fortune (Ex): At 6th level, you can reroll any one roll that you have just made before the results of the roll are revealed. You must take the result of the reroll, even if it's worse than the original roll. You can use this ability once per day at 6th level, and one additional time per day for every six cleric levels beyond 6th.
If the character rolls a natural 1 on an attack roll or saving throw, are they permitted to use this ability to reroll? Since a natural 1 in these cases are considered automatic failures, does that count as revealing the results of the roll?
Don't overthink it.
The answer is yes, they are permitted to use this ability.
If not, then by your reasoning, there are lots of other things they cannot use good fortune to reroll.
1. No rerolling damage rolls - the result is certain as soon as the die is read.
2. No rerolling any skill check with a static DC, such as a DC 5 climb check to climb a knotted rope.
3. No rerolling a Concentration check - those DCs are pretty much fixed before you roll the dice.
4. No rerolling any Save if the DM says "Make a DC 18 Will save". Just by his saying it that way you've lost your chance to reroll the die.
5. No rerolling to hit a monster once you've discovered it's AC. For example, Fred rolls a 19 and misses, Joe rolls a 20 and hits, so now as soon as you roll your attack roll, it's too late to use Good Fortune since you already know the result.
Suddenly, the range of things you can use this ability on becomes so minimal that it's almost not worth having it.