To answer the question there's really no way to match the defensiveness of certain people. That unfortunately is a personal problem that the individual needs to get over.
Part of the fragility comes specifically because, imho, we all picture ourselves as the hero of our own stories. And part of being the hero comes with having faced some great adversity for which we like to play the victim, even when we're not personally affected by something. As Wise points out with the "took our jobs" line, in most circumstances that wasn't a job someone had applied to or was currently in the act of working, just the perception that an opportunity was lost by you or gained by that person who may not have had the appropriate credentials strikes as some great injustice against oneself. "Why not me" tends to come with trying to rationalize about what's different between the individual and the other. Unfortunately, a good portion of people tend to look at it solely as "well it's because this person belongs to "x" race." Of course this isn't exclusive to race of course, hell, I've heard it enough in my industry that the reason why certain people get more opportunities than others is because of nepotism or any other number of things, which may or may not be true, but is the rationalization made almost instantly in order to paint oneself as a victim.
So when confronted with the prospect that they may inadvertently be complicit in the struggle of an entire race of people, suddenly now the victim is painted as the villain. That's a tremendous shot to one's own personal identity and character, which if we're being honest likely has less to do with those things as opposed to their lack of education about history, also something Wise points out. Someone's personal victimhood is so deeply ingrained, and these days stoked by people like Trump, that to be confronted with any other truth would be like me walking into a congregation and espousing the virtues of atheism. The only difference here is the church in the scenario of dealing with race is the Church of the American Dream. One in which most of white America, myself included, was taught at an early age the staples of "all men are created equal," "liberty and justice for all" and the virtues of a capitalist society that you can be and do anything you want if you just want it enough and work hard enough. The latter of which in most respects is true, though we aren't taught that some people are born with more of a head start than others due to any number of factors including race, socioeconomic status, etc.
But nuance isn't something that the majority of the public likes to consider. Things are much easier when they're black and white, no pun intended. Work hard and good things will follow. People exist on a totally even playing field in all aspects of life. These are truths many in the white community are led to believe. It takes people wanting to learn and understand the experiences of others with an open mind to be able to overcome their defensiveness and allow themselves accept that perhaps what they've been taught their whole lives and carried with them, potentially over several decades is wrong. But when someone lives a sheltered life where they're only truly exposed to a single demographic of people that's extremely hard to accomplish. Part of that is why I think college is constantly looked at as some great liberal institution, mainly because it forces people to be exposed to others likely outside of their demographic. I mean, there's a reason why people like Trump are popular with the poorly educated, and it's not just because people are stupid, but because those people tend to also come from homogeneous environments where the perception of the world passed down from their homogenized families for generations is never challenged. "How could anyone thing differently than this clearly correct line of thinking I've learned from the people I've trusted with my well-being for my entire life?" That line of thinking tends to extend unfortunately also onto the national level. "How could this amazing country I've been told forever is star-spangled awesome have such a grave injustice problem? Clearly it's others who are wrong." Otherwise known as the Seymour Skinner Rationale.
If the individual is not ready to internalize the possibility that something that they've known to be a fundamental truth is inherently wrong, then the fragility will unfortunately not be something that will be overcome. You may be able to make your points heard, but that's not a guarantee that they'll be internalized. It's hard to convince someone that their "team" is a problem when they themselves feel like their own personal struggle isn't something that's acknowledged.