A lot of coeliacs can also find it difficult to tolerate dairy and eggs but it isn’t impossible to bake dairy and egg free!
There are now lots of dairy free spreads available in supermarkets which you can use as a substitute for butter. In some recipes you can use Vegetable Oil or even Peanut Butter which is great in cookies and brownies.
For buttercream, I prefer to use Trex (Crisco in the US) instead of butter which makes a lovely light American style frosting.
Soya milk or Almond Milk can be used to add moisture to bakes instead of cows milk.
Instead of eggs I’ve often used Soya Milk in cakes to bind the ingredients together and used rising agents to help the cakes rise – if you want to know more you can check out my egg free cupcake recipe here.
Substituting 1 mashed up banana per egg works nicely in Brownies and Banana Bread. You can also make chia and flax seed eggs made from mixing water with ground up chia or flaxseeds!