Find a source for him ruminating on him being outspoken about his Objectivist beliefs outside of saying he wanted to adapt The Fountainhead.
EDIT: here, I'll help you research a little more about his political views by pointing you toward this very forum.
This conservative article is absolutely livid over Zack Snyder's political tweet | ResetEra
Ever wonder WHY conservatives would feel betrayed that Zack Snyder would take a side that wasn't with them, citing his body of work?
The strongest claim that people defending Snyder's political views are that he is a "liberal", his views don't cleanly map with Objectivism, and that he isn't fully in line with her political views. The politics of his films though do have conservative themes, even when the source material does not, so that is why people see his interest in The Fountainhead as some sort of indication of his political stance because some of it does make some sense of his creative choices in his films. The reality is that he may not identify as a "conservative" but many conservatives these days don't either, for many different reasons.
Even if he is left leaning, he's likely a center-left liberal, but I think it's more likely he consider himself a libertarian. He strikes me like a Joe Rogan centrist/libertarian type where he may happen to fall on the left side on some issues, but many of his views on the world and how he believes things work have a conservative bent since we see it time and time again how he views the world through the characters across his whole filmography. And like many centrists, by picking and choosing what things they believe in, it may lead to inconsistency in their world view, but while it may be unfair to frame someone like Snyder or Rogan as "alt-right", it also is disingenuous to treat them as "progressive" when they may have some views that skew hard right just because they may not be far right on issues like sexism and race.
I think for Snyder specifically, the criticisms about the politics of his movies are especially valid since he makes mainstream movies and reaches a wide audience, so people defending his creative choices by the fact that he doesn't have a deep understanding of the themes he invokes, isn't really a solid defense, regardless of how true it may be, since he keeps getting a platform and people have been saying these criticisms about his work his entire career and yet he doesn't approach things with more care having realized he is messy with his execution if that is not what he intended to convey with his creative choices.
Is it any wonder that criticisms have gotten louder now that he's been making movies for almost 2 decades and hasn't taken the criticism to heart and has an even bigger platform than ever? Not to mention that having the position to be the creative lead of a cinematic universe meant that his influence could have been bigger and suddenly more DC fans were willing to handwave any criticisms while also staunchly defending his work because he was in the position to give them something they desperately wanted.
I say this as someone who liked Man of Steel and has generally been a fan of most of his films, outside of BvS (never saw Dawn of the Dead or Legend of the Guardians): the criticism of his writing and themes have a lot of validity to them and always have. He's a cool visual director, he seems like a good guy and even well-intended, but his lack of understanding of themes that he tries to deliberately invoke is baffling at times and to say that some of his messaging is at best muddled and at worse problematic is and has always been on the money imo. I think his Clark in MoS is a misread of the character in an attempt to make Superman cooler and more "realistic", and I completely get why it rubs people the wrong way enough to ruin the movie for them when his dad basically teaches Clark that altruism is naive and that people, including yourself, will always get hurt if you try to help others. I get why the execution of Sucker Punch in it's female empowerment themes are mixed and even disgust people in the discrepancy between it's text and it's subtext. What I don't get is people trying to say it all doesn't exist or even if it does, Snyder is too dense or surface level to even understand what he is invoking (despite being someone who obviously cares deeply about symbolism and metaphor) to even attempt to criticize him or his work for any unfortunate execution.
