What can I do at my level to fix a toxic environment?

RP serves many needs, but soliciting answers to questions such as this must be at the top of the list. Thank you for reminding us.
I had a couple of minor incidents as a butter bar and was ill equipped to handle them. We spent a helluva lot of time in OCS learning weapons and tactics, but little about leadership. Those were lessons that would come with experience (usually the consequences of mistakes) and observing others. The fact that you've come here looking for answers gives me the impression that you haven't had any luck garnering wisdom and support from your superiors (or that you've hidden the problem from them - don't!)
Toxicity grows in quiet. You must acknowledge it and deal with it openly and honestly. "What we have here is a failure to communicate" is oft quoted from the movie Cool Hand Luke because it is so relevant.
There's little more I can offer without knowing more, however I will offer one last comment that may or may not apply. Your job as a leader is to provide your subordinates with the training, equipment, and clear direction they need to perform their mission effectively. They will work for you just as hard as you work for them. If they perceive that you are failing in your duty, the result may be perceived as a toxic environment

You fix what you can, as you can. But realize, take it to heart that you cannot fix the entire situation. Take care of your soldiers. Listen to them, show that you care and take the steps that you normally would were it any other unit. You make sure that you are part of the solution rather than the problem.

If there is fraternization you do your best to make sure that it is not happening with any of your soldiers. If a soldier under you has a profile you make sure that they know how to handle that situation and to speak up when the boundaries of it are stepped over. You do your best as far as planning going but understand you cannot fix the entire unit. Document, document, document and have your soldiers do the same. Sometimes you don't need to stop a soldier from going to the IG, you need to encourage it.

You take care of your troops. You take the bullshit sabot rounds coming their way. If they want to go to IG, let them.

I am not kidding when I add: PRAY to the other excellent responses here.

It depends on how far up the chain is toxic. If only in company unit, a letter to the Battalion commander could work (when sending/taking it in be sure you show cc: to IG). I did that and got immediate results without it ever getting to the IG.

First step is to identify the real problems. Soldiers like to complain about things, but that doesn't mean it isn't something that needs solutions. Here would be my approach. You have been there a bit, long enough to see how they perform, so I would sit down in a face to face counselling session with each soldier and tell them your expectations, what you have seen has their strong points and weaknesses, and to get their opinion of what is wrong, both personally and professionally, and what they think should be done. Make sure they understand that counselling is not punitive. I assume that your people are E-4 or below and that the UCMJ is Article 15. That should be in their local file if it has been under two years, I would read those just to have a bit of background. I would talk to my Platoon Sgt, First Sgt. and CSM about the situation and their opinion of problems and solutions.
That's the easy part. Then you need to list what is under your control and what isn't, and prioritize the things that need fixed. Pay, Promotion and Family issues should be at the top of the list. You can't fix a pay problem, but you can make sure that soldier gets to finance and make sure his problem is fixed, if he hasn't promoted, get with the readiness NCO and find out why. If they need schools, again, hit the Readiness NCO up and get them scheduled.
We each have to develop our method of leading, but make sure they understand the mission, make sure that they have been trained to actually perform it, then inspect or evaluate when it's done. If they don't know their jobs, then it's your job to teach them. You don't have to be a hard ass to be strict, but it is easier in the long run to enforce the rules as long as they are enforced evenly across the board.

Depending on how high the rot goes, you could try talking to either the BN CSM (risky) or the chaplain (less risky but with limited scope).
In either case, as a conscientious NCO your biggest challenge will be resisting the temptation to sink to the level of those around you and stop caring because nobody else does. The second biggest challenge will be to resist the temptation to side with your troops in anything and everything. Just because you are in a toxic environment it does not mean that you are not responsible for the good order and discipline of your subordinates. Disrespect, insubordination and insolence will be rife but you cannot allow infractions like these to pass without response.
This is when being a good NCO can really suck: when you feel a troop is justified in expressing dissatisfaction but you have to crack down because he expressed it in a way that crosses the line.
As a Non-Commissioned Officer in the US Army you have a responsibility to your troops, yes. But you also have a responsibility to your Unit and your Nation. Remember what you swore to defend and why the army exists at all. Then act accordingly. Yours is the face you have to look at in the mirror every morning. If you find yourself avoiding your own eyes, you are in serious trouble.

It isn't about them. It is about the unit and the mission. When your soldiers take more pride in the unit than their individual wants you will have something

#climatesurvey

If you think you have found Toxic leadership then by now you should know where and at what level that is happening at. That is the level you would need to work on to stop the problems that exist. Now i must tell you at this point i am a person that is hard to believe Toxic Leadership exist. Now if you truely have a issue of Toxic Leadership you will generally find a lack of communications at some level in the COC that is the hill you have to climb.
Examples is TEAM LEADER /SQD LEADER This level is pretty easy to fix by talking to those individual Leaders and if you get a lot of flak go to the Platoon SGT and have a chat. If it is a the Platoon Level Then you have to approach the Platoon SGT if that becomes a stopper then get the Platoon leader involved on and on up the COC. Now if you find that it seems you are fighting a loosing battle you may just want to let the Soldiers go to the IG.

Now with that said it has been misfortune to find out a large part of what has the Nick-Name (toxic leadership) is in fact A communication problem between the Soldiers and The Leadership that does not Garner IG level involvement. It does require communications between the most junior leaders and the next level of the COC. Some times it is just a lack of a posted Training schedule. Good luck and Tread Wisely.