I had a best friend who is ISFJ. She was incredibly stubborn and immovable on certain things. Once she was convinced of something, I don't think dynamite would move it. However, everything was always all about feelings for her. So if you can make your case using feelings as the be all and end all reasoning, perhaps that would help.
I have an ISFJ relative like this. She is extremely stubborn and the best way to get her to close her mind to anything is to simply suggest it. She's got really severe anxiety disorder issues. She is very inconsistent in her parenting, lets things go because she's too stressed to deal with them and then blow up and over-react. Now her children have behavior issues and need medications. She makes the most illogical, pure instinct emotional decisions of anyone I ever knew. I care about her but have trouble dealing with her.