That is a good point but there has to be a line drawn somewhere in order for the Justice League to retain its morality. Would the Justice League be willing to accept a White Nationalist or Nazi supporter into their ranks if they agreed to adhere to the rules of the Justice League? The very idea seems ridiculous and counter to the entire purpose of the Justice League. The problem is that if you will not accept human who simply support Fascist ideology than why will you accept aliens who actively support a Fascist government? It seems like the only answer is either double standards for human and non-humans or gross incompetence in investigating the suitability of members.
The answer to that, I think, is to deconstruct the scenario and look at it in more detail.
The main objections I have to this argument is that the actions of the Justice League aren't quite as simple as striving to follow a single morality, and secondly that a Fascist is not directly exchangeable with a Nazi in this situation.
For the first point, I doubt that the Justice League even has a unified morality that they try to follow, beyond the most basic of principles anyway. You aren't dealing with a unified body carefully considering if X is permissible, you have a bunch of individual members viewing things from their own perspective according to their own morals (which
do overlap to a degree), and raising objections if anything violates it.
They're like-minded enough that you still get general support for truth, freedom, etc, but there are still major deviations. Things like Batman, Superman, etc being
extremely opposed to killing in general, while people like Jordan or Captain Atom (who are/were in the military) are much less opposed to it in general, even if they abstain in their specific circumstances.
This model of individuals acting with loosely coordinated morals also explains things like why requiring unanimous votes for increased membership isn't viable in the long run. If they were completely unified and acting as a cohesive group, there'd be no issue; their membership requirements are strict, but not
so strict that they'd quickly run out of people who are admissible. But with a increasingly large number of individuals with varying morals who
all have to approve a new member, it's ever more likely that
someone will object. It's like trying to find a key that fits a dozen completely different locks.
So, now we've reduced the question to "why did none of the League members have enough of a issue with the Hawks to object?". That, I would say, probably varies a lot too. Some of the members probably didn't
strongly object to the Hawk's government from whatever brief description they got of it. It's not
obviously horrible until you look at some of the less publicized bits like the slums and xenophobia, and a lot of people probably wouldn't even apply the term Fascist unless they took time to stop and think about it. For others members, they probably just glossed over it a bit; things like "the Hawks are my friends, they seem like good people, surely it's not
that bad". And so on.
And for the second point, I object because Nazis and Fascists are not directly interchangable in this scenario. Obviously the League would
immediately object as a whole to anyone that they knew was a Nazi, or anyone else who isn't from the early 20th century who for some reason goes by a different name. But I doubt they'd immediately object to a Fascist quite as hard, for a few reasons.
First, if the Hawk government is Fascist, that means two League members are too. So they probably wouldn't object quite as much. Secondly, there is a
lot less disgust at the concept of Fascism than there is towards Nazis; no one except
them will support the latter nowadays, while you can find a fair few people who don't particularly object to, or even
want the former.
And building on that, Nazis are... weird. Not in a
Jetpack Hitler sense, but in a sense of how they've lingered in the public consciousness. They killed millions like cattle, relatively recent too, and nested in one of the largest conflicts in human history... and
Stallin wasn't and didn't? Or
Hong Xiuquan? History has little shortage of mass murderers. Hitler has a unique flavor in that he sought people out who were part of specific minorities using a guise of racism and pseudoscience, instead of using the more publicly-permissible excuses of 'civil war', or "they just starved, I dindu nuffin". But, still, it seems disproportionate; the other mass murderers are a footnote for a lot of people.
I would argue that the visceral disgust people feel at Nazis (or other various political-entities-who-are-at-least-20-years-old) are
not based on rationality or magnitude(
in it's entirety, they've still killed quite a lot of people), but a complex set of social factors. At the very least, if disgust was rational then you'd probably have more people who'd even realize what you're talking about when you
mention Taiping. So substituting a Fascist for a Nazi wouldn't make much sense, because a Nazi will always evoke massively more disgust than a Fascist all else being equal. And I even doubt they're equally dangerous in the at-least-20-years-ago political world; have the entire world forget about them both, and then see how far a outdated ideology based on proven-wrong pseudoscience and racism (in a climate of essentially
anti-racism) will spread, vs Fascism, which many people 20 years ago would earnestly argue for even though they
remember history.