> The point is that you could physically separate the organ from the body and just make the person take a pill with hormones. Unless you're some crazy Extended Mind Thesis guy who thinks that the environment is part of your mind, having an influence on the mind is not the same thing as being part of it.
The same could likely be said for pieces of the brain, if we had a way to synthesize the right substances. What seems much more relevant to me is whether the glands are directly controlled by the brain, in which case they are simply a kind of support organ, just like the heart; or if they have their own signal processing and can "decide" (in the algorithmic sense) to secrete substances based on their own analysis of the internal or external environment, separate from the brain. If so, then I would characterize them as a part of the mind. The fact that their function CAN be replaced by taking hormones doesn't mean that X+testicles would be the same person as X+testosterone-testicles: the part of their mind that decided WHEN to produce testosterone would be gone.
Note that this is all an IF. It's quite likely that the decision to release certain hormones in certain quantities is controlled entirely by the brain, with the glands responding only to nerve signals.
> Hormone replacement therapy seems like a pretty damn large change, but I don't think I've heard of a case where there's truly radical personality changes. The same goes for other gland issues and their treatment.
From what I know, there can be pretty extreme effects from hormone issues, like extreme mood swings and defensiveness related to child birth, for example, or extreme aggression/irascibility related to high testosterone.