You are dealing with three very different botanical entities here.
Peanuts are a legume, in the same plant family as beans and clover.
They grow underground as the starchy seed of a bushy herbaceous [i.e.
not wood forming] plant. A severe allergy to peanuts won’t be
stimulated by “tree nuts” such as walnuts, almonds, pecans, and
hazelnuts. However, people can certainly have serious allergic
reactions to tree nuts. But they would have to have two separate
allergies to react to both peanuts and tree nuts – they are not the
same thing at all. Tagua “nuts” are actually the seed of a palm tree,
and so are in a third, completely different category from the other
two. Much more like the pit in a date or a coconut than either an
almond or a peanut. I would be concerned if I had a serious coconut
allergy, but otherwise not. For further you should call a
good local allergy and asthma specialist in your area and ask their
opinion. Some additional working notes: Because tagua nuts are a seed,
the hard part of the nut is a starch. To work it effectively, you have
to file several holes in the brown outer covering and soak the seed
for several hours to soften it. The starchy nature of the seed means
that it burns easily if overheated by contact flexshaft burs or
sanding belts that are used at high speeds. This will smell like burnt
sugar [which it is], but isn’t toxic. Tagua is much safer and more
pleasant to work than bone or shell, but as with any small
particulate, wear a good quality dust mask while sanding, sawing, or
power carving the material. Tagua is very receptive to liquid dyes so
you can get terrific colors. I would strongly suggest sealing a
finished carving with either a hard carnuba wax or polyurethane spray.
I include tagua nuts in the supply packets for my flexshaft class
because they are such a wonderful way to learn to carve using burs.
So: go nuts!