Not sure about Christmas Cactus but our Parrot Club has reprinted an article this month regarding Aloe Vera. It says that Aloe has become very popular in the parrot world both as a spray and as an additive to drinking water to improve feather appearance. it goes on to say that aloe taken orally can be a laxative and it is a known carcinogen when given to rats, causing bowel cancers.
It reported a case in the July/August Bulletin of the Avicultural Society of America reporting an incident with an Eclectus parrot that nearly died after accidentally inhaling some spray and tiny oil droplets of a spray with aloe which ended up coating the surfaces of the lungs and air sacs, it resulted in a long recovery and a possible lifetime of problems because of it.
Here is a link to a fact sheet from National Institute of Environmental Health Sciences on Aloe Vera.
As it says in the end of the article in our magazine, if someone asks if it is ok to spray their bird with aloe vera, tell them it is not proven safe and you should not use it.
So when in doubt err on the side of safety and don't put anything that may harm your bird within their reach. Like with avocado, not all species of the fruit are toxic, but I am not going to test them on my birds to find out which ones are safe and which ones are not.