Sam,
 
This answer isn't going to be terribly scientific, as it's written at
4:20am, but hopefully it'll help.  (What can I say, I woke up early!)
 
A transplanted heart or other body part, even if all the tissue-matching
issues are as optimal as possible, is always recognized by the recipient's
body as a foreign substance.  With a really good "match" the rejection is
not as violent, but the rejection is always there.  It's a natural defense
mechanism.
 
To prevent/reduce this rejection, a transplant patient is always given a
huge array of drugs (which they will then be taking for the rest of their
lives.)
 
These drugs reduce the function of the immune system dramatically.  (After
all, they are meant to reduce the body's ability to recognize the existence
of a foreign invader.) This means that the person is ALSO quite more
subject to colds and diseases which their body would otherwise usually be
quite capable of coping with.  It's called an immunosuppressed state.
 
So, much like a person with HIV or active AIDS, taking steroids, or on
long-term antibiotics, your friend is going to be much more likely to
catch diseases from his pets.  One example of this (though I'm sure the
veterinarians in the audience can come up with far more and better
examples) is toxoplasmosis in cats.  While it's frequently present, our
immune system normally is such that we never get sick.  AIDS patients,
however, can and do get toxoplasmosis, and other far stranger and weirder
things that most of us have never heard of because we usually never get
sick with it!  Kaposi's sarcoma (the black skin spots AIDS patients get)
used to be unheard of except (if I remember rightly) in elderly Italian
men.  PC pneumonia (a very rare kind of pneumonia.) And so on.
 
At any rate, IMHO your friend's doctors told him to get rid of his pets
because of the medication he will be on.  It's a hard decision to have to
make.  I don't know enough about the meds to say whether some compromise
could be made (I doubt it thought) but any such thing would have to be
done with full cooperation with his doctors, lest it endanger his life or
well-being.
 
I too would like to hear about anyone else's experience with this (at least
to the extent that BIG will allow it, topic-wise); I'm certainly not a
transplant expert.  (And I haven't had my coffee yet, either!  ;-))
 
Hope this helps your understanding, Sam.
 
- Megan
[Posted in FML issue 2544]