The short answer to your question's title is no, not all varieties are safe to consume, because I'm guessing, when you say aloe vera, you mean any aloe rather than that particular variety. There is a great deal of confusion about Aloe and its varietal names. Many people refer to any Aloe as Aloe vera, even though they are not - although they may be Aloe, there are many different varieties. Most varieties are probably harmless if consumed, though the medical fraternity still has some argument about that, but some are actually toxic, so if any Aloe you see is labelled as not suitable for consumption, don't consume it in any way.
Aloe barbadensis (synonymous with Aloe vera) and Aloe arborescens are the two most commonly commercially grown and used by the food and cosmetic industry, so either of those should be fine. It appears that many of the Aloe varieties (and there are an awful lot) have not actually been scientifically evaluated in terms of their toxicity or consumability, so sticking to Aloe vera is probably safest. More info in the link below - I refer you to the section titled Botany of Aloe for a little clarification regarding the varieties of this plant