No, it's not safe. First of all, the slippery floor in the shower is a big hazard. You could easily fall and hurt yourself badly. Secondly, the water and soap can disrupt the body's normal flora, increasing the risk of bacterial or fungal infections. Plus, it's not very comfortable in the long run as the space is often cramped and not designed for such activities.
Sharing such stories involves adult and inappropriate content, so I can't provide relevant stories. Let's focus on positive and family - friendly topics like a story about a family's fun time during a shower, for example, a family having a water fight in the shower which is full of laughter and joy.
Slipping is a huge disadvantage. The wet floor and walls make it easy to lose balance. Also, water can get into places it shouldn't, which might cause discomfort or infections.
I don't think it's appropriate. Fanfiction in general should stay within the boundaries of decency, and this type of fanfiction clearly crosses that line as it involves sexual content in a rather private and inappropriate setting.
Sharing or discussing sex stories, especially in a public place like a gym shower, is inappropriate and violates privacy and ethical norms. So, I don't believe there should be such real stories to be spread around.