Mushrooms have a mix of IF and SF, so if eaten carefully with a good SF base, they should be fine. Shiitakes and creminis are especially good for you, and I've found cooking with creminis give the dish a meatier flavor, which is nice.
Yep, avocado is high in fat -- how do you usually eat it? I usually have 1/8 - 1/4 of an avocado in a sandwich or taco without any problems.
I think both of these foods are important to include in your diet, if you can do so safely.