I'm asking this question because in my mind, if all the Subjects of Ymir came from the same 2 people, then all of their descendants should have Royal Blood and should be able to use the power of the Founding Titan (such as Eren Yeager).
I can only partially answer the question. However, I believe the most recent episode I watched (From You, 2000 Years Ago), makes some things clear about how the power of the Founding Titan works. The main point to is that the original Ymir exists in some capacity inside the Coordinate, as a conscious entity. To control the power of the Founder is the same as to control this entity. During her lifetime, Ymir was shown to be loyal to King Fritz, for whatever reason. It's probable there was some form of brainwashing going on, though probably it wasn't even done on purpose. Rather than brainwashing, it could also be thought of as mental conditioning or trauma etched into her mind, which made her go along with whatever Fritz, her master, told her to do. We hear someone's voice telling Ymir she should strive to be of use to the world, to make it a better place. Ymir lived her life as a slave, and she continues to exist as a slave even after she died. Her loyalty, or rather, subservience to King Fritz must be deeply ingrained in her mind.
According to the wiki page for Subjects of Ymir, it is in fact stated that the Subjects of Ymir, those who can become Titans, are indeed all descended from Ymir:
The Subjects of Ymir (ユミルの民 Yumiru no Tami?) are an ethnic group descended from Ymir Fritz and the only race that was capable of becoming Titans. Beginning with Ymir and her three daughters, the bloodline eventually expanded across the Eldian people, to the point of majority.
Then what is the distinction between those of royal blood and the ordinary Subjects of Ymir? We actually don't need to understand that. All we need to know is it is a distinction Ymir makes. Whether it's real or not, Ymir understands the distinction, and only obeys those she views to be of royal blood. It's even possible it was something imposed later, much like the vow to renounce war, something burned into Ymir's psyche to be passed down. But we can infer, whatever the case, that Ymir is the gatekeeper here. Once you have a thinking entity gatekeeping, rather than some law of nature about blood dilution or what have you, anything can happen, especially if the gatekeeper has as broken a mind as Ymir's, and mistakes might be made such that the "rules" don't actually make sense. Whatever the rules are, they make sense to Ymir.
Also, it isn't true that the royal bloodline starts with Karl Fritz the 145th. As I understand it, the reason Zeke is supposedly going to be able to control the founding titan without having to worry about the vow to renounce war is because he's a member of the royal family that isn't descended from this King Fritz. From Dina Fritz's wiki page (Zeke's mother):
In the year 824, Dina first appears as a person sent to the Eldian Restorationists by "the Owl," an unknown mole in the Marley government working for them. She introduced herself as a member of the royal family. It is explained that a branch of the royal family refused to flee to Paradis Island with King Fritz at the end of the Great Titan War and Dina was the only remaining member of that group.