Is it okay to freeze banana puree and avocado puree?

You can, however I prefer not to as they oxidize and turn brown. Texture is also changed. Best to feed fresh. With avocado, if you can't finish the whole thing, then just put the skin back on, wrap it with a cling wrap, put it in a tupperware and back into the fridge. If it turns abit brown, you can just scrape off the top part :)