1) I study conflict resolution with a focus on organizational conflict
2) I gossip like a motherfucker
Personally, I take these things to be indicators and try to take a qualitative research tack. What nodes keep popping up? If everyone says Carol is a bitch, what's up with that? As for shame, what's going on there? Maybe digging into those feelings through something like writing out your thoughts (by which I mean, writing without self-judgement in an effort to map feelings, tensions, and potential inciting incidents) might be helpful.
I don't know your situation, particularly as some of the information is apparently sensitive, but I am curious about the role of leadership within your organization. What kind of leadership exists? Are there underlying sources that result in gossip? Can you talk to anyone in the leadership about this? What avenues exist for you to try to address this issue of morale?
Often, with top-down leadership, there is a great deal of power distance, resulting in a lack of employee buy-in, inclusion, and belonging. In organizations where power-distance is minimized and employees tend to have a lot of trust from their leadership, we see a lot of decision-making ability and thus, empowerment. When people have this ability, creating employee/"follower"-based solutions is often an option, which tends to improve morale.
In my view, gossip tends to occur when people don't have outlets that are sanctioned as legitimate for grievance within organizations. Often, this results in employee turnover, a lack of trust, and overall, greater expenditures in training and ineffectual interventions, such as diversity and inclusion programs rooted in compliance to Title VII and affirmative action, as opposed to employee empowerment. We also see litigation more often in these types of environment.
In short, avoidance of gossip or conflict tends to have adverse effects. However, engaging in conversations to address morale can also have adverse effects for employees as organizations are inherently conservative and interested in avoiding litigation and so may be prone to retaliation or attempting to sweep things under the rug. Of course, my advice would be to seek the help of a professional; a facilitator, a mediator, or someone who can help with conflict, but then, I have an interest in promoting the industry I'm hoping to be employed in. The one thing I can tell you, is that there is no need to be ashamed for feeling like things can be better, or for regretting a contribution to negative dynamics. It sounds like you have a clear idea of what the problems could be and that there might be a real need to address them. Who can be engaged to work this out?