In all honesty, I'm not entirely opposed to the idea of the Croft family having a wild reputation, a few explorers in their lineage, and a couple of members involved in a secret society for aristocrats and nobles. However, I imagine that each Croft is vastly different from the last, so every one is their own distinct individual that's merely connected by the family name, high social status, and biological similarities. Every Croft has their own personalities, motivations, opinions, and so on. This explanation also helps Lara stand out from the other Crofts, such as her father who disapproved of her thrill-seeking lifestyle and her refusal to marry a nobody of noble status to pursue the excitement of discovery and adventure.
Even if Lara's family has a troublesome bloodline, includes a few famous figures, and was involved in certain crimes, making her family lineage narratively and thematically flexible would still let her keep her uniqueness. Lara is still connected to her family in some way (e.g. being an aristocrat), but when writing the Crofts, they should have enough separation that she stands out among her long bloodline. I've always viewed her as the defiant outlier among the Crofts. There's a possibility that other Crofts were also rebels, but applying the logic I've introduced in my lil' opinion piece, their reasons would be far more different from Lara's. Lara doesn't need to be tied to a secret society, family drama, and an ancestral drive for exploration because all of what's laid out in the letter written by T.E. Croft completely defeats the purpose of her character as a revolutionary, a fighter, an explorer, a thrill-seeker, and an autonomous woman not bound by the stifling expectations of high society.
Some bloodlines are marred by atrocity and simple unpleasantries, and I think it's okay to explore those serious implications. However, Lara shouldn't be so fiercely tied to her family like it's a fucking curse she can't escape from. She should be able to stand out from her family members and ancestors. She should be one of many Crofts who's still her own person, redefining what this unpredictable, hard-to-describe family can be.
Expectations and biological ancestry mean nothing to her regarding the Croft family. She chose to distance herself from the family name to be herself because she didn't wanna be the person her parents wanted her to be. She made plenty of friends who had immense respect for the crazy, badass lady she is! For crying out loud, many of her rivals and enemies also show some begrudging respect for the legacy she carved out by refusing to be a conformist and proving herself to be a capable explorer and fighter! For example, there's Winston, her forever faithful and humble butler; Jean-Yves, an Egyptologist friend who willingly helped her avert apocalyptic disaster back in Egypt; Mark Willard, a Doctor of Science that was astonished by her success in retrieving the Infada Stone and hired her for her competence to fulfill his misguided, obsession-fueled goal of advancing evolution on a global scale (It's important to note that in the manual for Tomb Raider: The Lost Artefact, it's implied that Willard was a fan of Lara and her pursuits!); and Eckhardt, an enemy of great alchemical and sorcerous power who goes out of his way to genuinely compliment her abilities, even though he and Karel were deliberately using her to obtain the Obsurca Paintings.
Overall, I'm genuinely disappointed by the revelation of this letter, and I fully agree with the statement @sharksmirk took the time to write. Crystal Dynamics clearly has no idea what they're doing with the TR franchise. They refuse to write a Lara Croft who truly feels like her classic self; instead, they're trying to reshape her to match their misguided, self-absorbed opinions and their flawed understanding of the world.
