Number conservation of bosons and fermions

If what you mean by conservation of "number of fermions" is that the number of fermions in the initial state must be equal to the number of fermions in the final state, well, it's wrong. Consider for example this nuclear reaction (which exists):

$$p + p \to \pi^+ + d$$

where $p\equiv$ proton (spin 1/2), $\pi^+$ pion (spin 0) and $d\equiv$ deuterium (spin 1), you see that there are 2 fermions in the initial state and none in the final. So no conservation of both the number of fermions and the number of bosons!

What is conserved by all reactions (so far…) are:

1. Total angular momentum (and not only the spin)
2. Energy/Momentum
3. Total lepton number
4. Baryon number
5. electric charge

(plus the symmetry CPT but it's a bit different the context of this question).

Now, one can define the fermion number as $B+L$ where $B$ is the baryon number and $L$ the total lepton number. Its conservation is a consequence of the conservation of both $B$ and $L$ individually. But beware that fermion number doesn't mean "number of fermions".