My son tells me not to tell his dad things

My child’s father is honestly way more strict and harsh on my 5 year old than I am. I try to go with the gentle parenting approach when it’s needed and whenever I’m around him and my son, he is constantly raising his voice at him. Most of the time he is raising his voice at my son in situations that I have also been in but I’ve been able to redirect my son or talk him through whatever the problem is. Or talk him into listening. Now my son is telling me not to tell his dad things. For example, we were getting ready to go somewhere but his dad was still upstairs getting ready. I put my sons shoes on but a minute later he said his foot itches and he needed to take his shoe off to scratch it. He told me “don’t tell daddy” and then after he was done scratching his foot he was begging me to put the shoe on quick before his dad noticed he took it off. He was saying “please please put it on quick”. Another example was his dad told my son not to talk about something (I won’t say what because it was personal) but when his dad left the room my son brought it up and said “don’t tell daddy that I talked about it”. Honestly the way he talks to my son makes me so mad. I feel like it’s completely unnecessary and it’s making my son literally scared of his reaction to such small things. I don’t even know what to do about this

Eta- I DO stand up for him, I’ve explained to his father over and over that it’s completely unnecessary to raise his voice and that just talking to him is enough he’s a very smart kid and sometimes just needs to be explained things because he’s curious and inquisitive. I tell him that all the time honestly I’ve considered that he either needs parenting classes or I should just go for full custody if he can’t change.