The consequences of gendered institutional toxicity manifest in both internal and external ways, and have a detrimental effect on organizational performance at both levels.
If, for example, an organization actively refuses to promote women to management positions, this has multiple negative effects. On a large scale, it creates tension within the organization that can cause interpersonal conflict. On an individual level, it fosters resentment among the women whose careers are passed over in favor of their male counterparts. Crucially, it also robs the organization of the potential to have a diverse set of perspectives and experiences represented at a management level. If everybody in charge has the same professional background and life experience, an organization is only well-equipped to handle the problems that people with that one background have already encountered. With a more diverse network, the organization has a much broader wealth of experience to draw from.
The same dynamics can be engendered by toxic masculinity. If an organization puts a higher value on a man's ability to adhere to their idea of "manliness," he, too, might feel resentment towards the organization and tension among his colleagues.
Even if you don't experience this particular type of tension in your life, think about the conflicts that you do experience and what impact those have on your own personal productivity. Any time you're angry or upset, it becomes much harder to thoughtfully complete even the most basic tasks in your life. This is true whether you're trying to write a research paper, or put in a contact lens, or empty the dishwasher—if a certain percentage of your energy is now dedicated to fixating on those feelings, you have less energy to dedicate to what you're trying to do. If you have less energy to put toward your work, it has a detrimental effect on your productivity.
It's certainly true that there are people out there who thrive under pressure and seek out environments of conflict, and it's impossible to say universally that everybody in the world has exactly the same needs all of the time. For the most part, though, the majority of people benefit from an environment where they're free to focus on the work at hand instead of their frustration in the workplace.