If you can't join them, beat them.
The Galactic Federation has a REALLY big flaw it it's basic concept... even bigger than the Immune system issue. Thier absolute prohibition of killing means they have no concept of military doctrine, weapons technology, or antibiotics... and even if they could figure out how to weaponize any of thier technology, they would be ethically prohibited from doing so.
So, if they won't give us a seat at thier table, we can just bring our own... or heck, we could just take the whole damn table. What are they going to do to stop us?
No matter how primitive we humans may be compared to them in all other realms of technology, we are millenia ahead of them in at the art of killing things; so, all we need to do is fly around to all thier planets, bomb them into surrendering, and then we get to steal all of thier advanced technologies and rule over the entire Galactic Federation... ehhm... I mean the Human Empire, ourselves. No more Galactic Federation, no more need to figure out how to stop killing things.
Could they Fight Back?
Military technology is always a bit different than its non-military counterparts. A generator is fundamentally different than a cannon. A nuclear bomb is fundamentally different than a nuclear reactor. And a rocket ship is fundamentally different than a guided missile. A civilization forbidden to kill will have all sorts of missing infrastructure and research that will make militarizing thier tech a long and difficult process. Especially if thier scientists haven't already spent thier whole lives sitting around daydreaming ways to weaponize thier tech like humans do. Trying to figure out something as simple as making a missle will be like modern man trying to figure out Roman Concrete on Damascus Steel. For all of our chemistry and scientific tools, these were still a multi-decade processes because we don't think the way these Ancient civilizations did, and we simply did not know what we did not know.
The transition is made especially hard for a civilization that is committed to doing no harm. Thier entire techstack that they have been working on for countless generations would be full of failsafes designed to prevent either accidental or intentional harm. Let's say they try to take an existing ship and fly it into Earth as some sort of improvised doomsday weapon. The central AI will take over and course correct. So they have to redesign and train a new systems AI that is able to kill... except your standard SDK will recognize that you are making a dangerous AI; so, it won't let you compile forcing your to make your new AI from scratch using old, slow, and mostly forgotten programming techniques.
Oh, but what about the chip-set (or alien equivalent) that ship AIs run on. Those likely have hard-printed fail safes in them to prevent AIs from killing too; so, you'll need to design and manufacture new hardware to run your killer AIs on too. Oh, and don't forget the star-drive has a built in gravity detector that will manually override the AI if the ship gets too close to a planet; so, they have to design a whole new star drive control system too. Oh, and did I mention thier navigation array also has a failsafe that will EMP the AI and shut the reactor down if the AI tries to plot a course that intersects a star or planet.
While this may sound excessive, a good analogue to this would be the the Apollo Missions. After the Apollo I disaster, NASA adopted a thier own engineering doctrine of doing no harm. As a result, by Apollo 11, many systems had 6+ redundancies in place to reduce the risk to life as much as possible; so, with something as dangerous as a ship that could depopulate a whole planet, these aliens will have every backup in place they can imagine to stop themselves from misusing the technology they have as a weapon.
All of this together means that to make a weapon against the humans, they need to design thier new weapons and infrastructure from the ground up having no idea how exactly weapons really work. It would probably take them 10-20 years just to make a basic ballistic missile. Making one that can get past human active defensive that we've been RnDing since the mid 20th century: even longer.
Would they fight back, even if they could?
All of this is a moot point if the aliens don't even choose to fight back. While they may follow the no killing rule, at least some of the member races will have experience with dangerous predators and parasites meaning that maintaining this doctrine will come with the acceptance that sometimes a primitive, less evolved species will come along and kill one of them. So, a necessary part of this doctrine will need to be "Not even for self-preservation". If you allow killing for self-preservation, then humans as a whole would have no problem joining the Galactic Federation as we are now, and the whole question is a non-issue, but if you disallow it, then we primitive humans would just be seen as no different than a particularly dangerous species of wolf.
They would do thier best to avoid us, hide from us, contain us, relocate us, etc., and they could actually be very good at it, but every once in a while, we'll find a way to catch them off guard. But unlike wolves that occasionally steal a lamb: we are stealing ships, lab equipment, blueprints, research notes, and star-charts. Eventually we'll learn enough of thier technology that our non-military tech will all catch up, and our military tech will be far more advanced than anything they could improvise last minute when they realize that they can no longer keep us contained.