I think everyone who has answered thi has totally misunderstood the OP. their parents, as far as I can see, are not trying to restrict their food intake so much as stop them eating what they deem too high in fat, cholesterol, mercury or whatever. Or simple excessive- and yes, five avocados would be probably too much of one thing! It sounds like they're not wilfully trying to keep you underweight, they just think you should eat a diet higher in carbs (which is the same as eating less animal products).
Basically your parents are questioning the premise of paleo, or the anti-candida diet, whichever. Like many others they might not "believe" in candida. Have you explained it to them? Have you found hard evidence as to why more than one egg a day isn't going to send your cholesterol skyhigh, and evidence as to the same for meat and fish?
If you have tried to explain and they refused to accept it, then you have to move onto taking control of your own idea. I thought I had candida last year. I am no longer sp sure, but I was 100% convinced and extremely stubborn about it at the time. People suggested that it didn't exist and that only terminally ill patients have it, and I refused to believe them, insisting that my symptoms matched. I want to know who diagnosed you and what symptoms you have, but I am not going to tell you that you don't have it or that it doesn't exist.
I can really empathise however with the "fear" if food as I thought that anything could make me sick- even carrots!! I think the stress over worrying about "candida causing" foods only exacerbates whatever is up with you, and particularly your digestion. So firstly, try to chill out a bit and don't go madly hunting on the Internet for the million candida diets that are out there.
What you CAN do is try to keep yourself nourished. That is number one with candida or similar ailments. do your parents buy all the groceries? Is that another reason why theyd be upset if you ate a lot of protein and avocados? Assuming that you have some money of your own, invest in some virgin coconut oil (it's antifungal and anti parasitic as well as being high in calories and very good for vitamin absorption). Buy canned fish, your own eggs, whatever it takes. Even if you live with your parents and they refuse to agree with your diet, you can implement it yourself. Eat butter-slathered vegetables. Other dairy products and nuts are not great for candida-like symptoms so focus ok animal fats and coconut oil. Good luck.
I wonder if it is fear of exacerbating the candida rather than fear of eating or gaining weight itself- that's why it sounds like anorexia in the medical meaning of not eating rather than the pathological disorder of anorexia nervosa. Maybe.
Nuts amd dairy are usually contraindicated if you have candida as they are considered "dampening" foods. Coconut oil, however, you can have in spades, and butter is okay too, so go for that.
If it is your parents paying for the pod them perhaps that's another reason they don't want you eating so much meat etc. If they are unconvinced about candida try at least to explain to them the reasons why eating more eggs, meat and fish is not unhealthy. If you can buy your own food then do that- canned gosh for example and coconut oil would be a great place to start.