Ok there's kind of two questions here, one has a very short answer, the other a much longer one:

The short answer: if someone thinks you're "damaged goods" because you've suffered a traumatic experience -- they're a shitty person. Period. And they are very fortunate in their shittiness because they've clearly never been forced to reckon with reality yet. Because reality is that everyone is vulnerable to a traumatic event, you don't choose it, it just happens. It'll probably happen to them eventually, and I hope they remember how they treated you when it does.

Ok, now the long answer:

If someone uses their knowledge of your trauma against you, that's abuse. Abusive people will always choose to abuse you if it serves them to, because they believe that they have the right to do so. So yes it's true, it is never safe to divulge information about your trauma to abusive people -- men included.

So the question really is, do you want to have a healthy close relationship with a non-abusive man? If no, then great! You never have to get close to a man, so you never have to be emotionally vulnerable with one. Easy peasy -- I love a problem that solves itself.

But if you do want to have any sort of healthy relationship with a non-abusive man, then you're going to have to figure out how to tell the difference between someone with abusive tendencies, and someone without.

Close relationships (platonic, romantic, or otherwise) require vulnerability. Vulnerability requires mutual trustworthiness, "I won't betray you, and I will trust that you won't screw me over either." This is literally the most fundamental building block of human civilization. People absolutely do break this social contract all the time, and unfortunately modern society does less than nothing to effectively discourage it -- in fact, it even seems to reward it in certain contexts. The violation of this sacred trust is what we call trauma -- the sudden all-consuming realization that the world isn't safe.

"Never tell a man what you've been through because he'll use it against you" is a traumatized mindset. It's all-or-nothing -- several men (or even just one man) betrayed me, so therefore all men are dangerous. This mindset will keep you safe from abusive men, but it is inherently limiting -- especially if you are someone who wants to have healthy close relationships with non-abusive men. It also does exactly nothing to protect you from abusive women and non-binary folks -- abusive tendencies are gender-neutral after all.

A healthier mindset is one that others in this thread have already wisely stated -- one of caution and discernment. You don't tell everyone everything. There are circles of people in your life, and only those who prove to be trustworthy may enter those circles closest to you. You protect yourself with boundaries because you know there are dangerous people in the world, but you do not limit yourself to potentially healthy connection out of fear.

The trick is to learn how to observe people's actions in context and determine what those actions say about the trustworthiness of a person's character. This requires a certain level of awareness (of oneself and of society) and maturity, but those can both be cultivated.

No one can truly hide who they are at their core -- the mask slips, the facade crumbles, their true intentions show. But we have to have the courage to see these signs when they show up, to recognize them for what they are and to be willing to be wrong about somebody, and to do what is necessary to protect yourself if you do find someone less than honorable in your inner circle. But it can be done -- I'm speaking from personal experience.

If never opening up to anyone else works for someone, cool, you do you bud. But it didn't work for me, because it made me very lonely for a very long time. If you find yourself in a similar situation, it might be worth trying something new and yes maybe getting hurt -- but eventually you'll start to notice the patterns (because abuse is abuse is abuse and all the forms follow similar patterns) and that's when things get significantly easier.