The first problem with your reasoning is that you're asserting "there are limits to empathy" as if it's an unassailable maxim, rather than an assumption grounded in nothing. Presume you're right - I can never fully empathize with the experience of an Uyghur in a concentration camp. So fucking what? Can I empathize with an Uyghur in a concentration camp enough to put myself in their shoes?

Oh, but I can understand an Uyghur in a concentration camp, I just can't fully empathize with them. Because understanding and empathy are different things, and somewhere nebulous where we don't know where it is it ceases to be empathy and becomes understanding.

Let's talk Anne Frank. Neither one of us is a fifteen-year-old Jewish girl. We cannot have "perfect" empathy for her experience. But which of us has more "empathy" and which of us has more "understanding?" By blood, I'm an Ashkenazi jew. Never mind that I grew up completely divorced from the Jewish experience, under Nazi rules of engagement I was destined for the camps. But I'm also a blonde-haired, blue-eyed Nordic-lookin' sonofabitch so it probably wouldn't have cost me beer money to get that cleared out. You, on the other hand, have a Polish surname. Maybe you have a better understanding of Anne Frank's experience. But maybe Tomi Lahren has a better grasp of the Anne Frank experience because she was once a 12-year-old girl. I'm sure she would cheerfully subscribe to your reasoning: what you're doing is eliminating the effort and obligation of understanding those with a different experience by arguing it's scientifically impossible (at some nebulous point best left to theory). This explains why Trevor Noah's gutting of her philosophy shouldn't be considered - he can understand with the condition of being a 20-something blonde racist with rich parents but as a black South African he'll never truly empathize with it.

More importantly, though, where's the utility of your discovery? Presume you're right. What does that get you? You're injecting a purity test so that you can stomp other people. It will not surprise you to discover that I've encountered this reasoning before: A white dude living in New Zealand who's been a lifelong member of the Freemasons and who has an MFA in acting from USC told me to "check my privilege" as a way of arguing that JD Vance was full of shit (PROTIP: he is):

You've basically independently discovered intersectionality bingo: not the concept of intersectionality, but the practice of stacking your repression credibility in order to win an argument instead of using logic, reason or evidence. He who is most oppressed wins the discussion because nobody else can truly empathize with their struggle and whatever you're talking about, you can easily make it about struggle.

You have discovered nothing useful here. More than that, what you think you've discovered is useless nonsense. Let's get to the true problem:

I felt the need to write this, because I've been trying to better understand why some behavior that ostensibly aligns with my ideals feels disingenuous to me.

I will bet you anything it's because you've been watching a few games of intersectionality bingo.