I wouldn't let them stack, saying they are from the same source... but that's just me.
They are 3rd-party Bloodlines, anyways, so it's all kind of up to the GM to make that $#!+ work.
Like the Righteous Bloodline's Spell Smite... add your Charisma to the DC? What, again? You're a freaking Sorcerer, you already add your Charisma to the DC...
It might be sorta like multiclassing of paladin, divine fighting style for Desna (not lore legal but I digress), and oracle battle mystery to get charisma 2-3+ times to things, where you can "have charisma as a bonus, a bonus equal to your charisma, and a specific typed bonus also equal to your charisma" to get around common sense stacking cheese?
It might be sorta like multiclassing of paladin, divine fighting style for Desna (not lore legal but I digress), and oracle battle mystery to get charisma 2-3+ times to things, where you can "have charisma as a bonus, a bonus equal to your charisma, and a specific typed bonus also equal to your charisma" to get around common sense stacking cheese?
Yes, but those each provide their own avenue to stacking shenanigans. As you mentioned, their wording differs enough to argue they are from different sources.
This is one Sorcerer with two Bloodlines. Regardless of having two Bloodlines, they have but one class feature called Bloodline Arcana. I find it dubious, at best, that one could even argue this is from multiple sources. Both fall under Bloodline Arcana, and Crossblooded didn't change that. Both say "your Charisma modifier"... which would also be the exact same source.
Their stat block would read:
SQ bloodline arcana (add your Charisma modifier to all of your saving throws, add your Charisma modifier to all of your saving throws)
It doesn't even look good, or make sense once projected into a stat block. It's all 3rd-party garbage, anyways, so good luck making any of it work right.
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As VoodistMonk said, they don't stack.
Do ability modifiers from the same ability stack? For instance, can you add the same ability bonus on the same roll twice using two different effects that each add that same ability modifier?
No. An ability bonus, such as "Strength bonus", is considered to be the same source for the purpose of bonuses from the same source not stacking. However, you can still add, for instance “a deflection bonus equal to your Charisma modifier” and your Charisma modifier. For this purpose, however, the paladin's untyped "bonus equal to her Charisma bonus (if any) on all saving throws" from divine grace is considered to be the same as "Charisma bonus (if any)", and the same would be true for any other untyped "bonus equal to her [ability score] bonus" constructions.
Both say "You add your Charisma modifier to all of your saving throws." and the rule about stacking and the FAQ that makes it even more explicit prohibit them from stacking.
The crossblooded sorcerer your GM is making has some family problems "Righteous Bloodline and Corruption Bloodline" at the same time. What she is, a Forlarren?
Ah, I wasn't able to see the full wording and was just adding the possibility.