I don't think your MIL is "carrying on". I think she has really listened to you and is struggling to understand your point of view. She thinks you feel this way because you are accusing her husband, rather than it just being something you don't like. I think you need to have more of a conversation about it so that it clears the air around anyone suggesting any wrong doing towards your husband or your son. It isn't about her husband/your FIL, it is about your preferences as parents and your husbands preferences when he was a child.
My son loves showering with his dad, but your DH clearly didn't - horses for courses!
If my son really wanted to shower with his grand father I wouldn't forbid it, but it would have to be at my sons request rather than the other way around. I don't want to hide nakedness from my kids but I don't want to force it on them either. I was always naked as a child and frequently invaded the "personal space" of extended family as I just didn't see why people would be uncomfortable with it, but that's me - my husband is the complete opposite!
At the end of the day it comes down to personal preference and what you are comfortable with.
I do think you need to do some work on clearing the air with your MIL and FIL as this is a very sensitive topic (as it is very easy for people to quickly head towards pedophilea etc, which I don't think is what you are suggesting your FIL is). As you have just moved to their state they probably aren't super close to you as a family and it will take work and a lot of mutual understand to get familiar with each other's preferences.
Now that you have said something it shouldn't happen again, but it would be a shame for a difference in parenting preferences (which is how I am taking your OP) to get in the way if developing a close relationship with your inlaws.