Are electric charge $U(1)$ and baryon number $U(1)$ parameterized by the same phase? Both of them are described as conservation due to the symmetry of an overall phase change (to the same spinor, I assume). But yet they are different properties.
Another way to ask this question is: can the phase related to electric charge conservation and the phase related to baryon number conservation be added or substracted?
 A: If we rotate the phase all charged particles by an angle $\theta$ times their charge, and rotate the phase of all baryons by an angle $\phi$ times their baryon number, then the Lagrangian is invariant (hence there is a symmetry).
Let's consider one field $\Phi_1$ (of any spin) with charge $q_1$ and baryon number $B_1$. Then under the joint charge and baryon transformation, this field transforms as
\begin{equation}
\Phi_1 \rightarrow e^{i q_1 \theta} e^{i B_1 \phi} \Phi_1 = e^{i (q_1\theta + B_1 \phi)} \Phi_1
\end{equation}
So in that sense, the rotated angles add.
However, take another field $\Phi_2$ with charge $q_2$ and baryon number $B_2$. This field transforms as
\begin{equation}
\Phi_2 \rightarrow e^{i q_2 \theta} e^{i B_2 \phi} \Phi_2 = e^{i (q_2\theta + B_2 \phi)} \Phi_2
\end{equation}
There is no way to write the rotated phase of both $\Phi_1$ and $\Phi_2$ as (some field-dependent constant) times (one field-independent angle). There's nothing wrong with this, but it reflects the fact that these are two separate symmetries as opposed to one larger symmetry. In other words, symmetry group is a product of simpler symmetries $U(1)\times U(1)$, rather than being a 2-dimensional group that cannot be decomposed into simpler pieces.
On the other hand, if we only consider a charge rotation, or only consider a baryon rotation, we can consider the transformation to involve one parameter which is universal for all fields undergoing the transformation, and a set of constants for each field.
