You might be confused. Ignoring the sign complication for the moment (having to do with SU(2) conjugate representations), consider the rotation group, in the "addition" of angular momentum constituents/components.
A total spin 0 singlet state composed of two spin 1/2 constituents,
$$\frac{1}{\sqrt 2}(|\!\uparrow\downarrow\rangle - |\!\downarrow\uparrow\rangle),$$
is really a superposition of two spin 0 states with eigenvalues S=0, and $m=0$. Such states may mix and interconvert.
- Similarly, you are superposing two middle ($I_3=0$) states with isospin 1 (isotriplets), and $Y=0$, so Q =0. These two states my interconvert into each other, and so they can mix and superpose.
Raising the isospin gives you a Q=1 state,
$$
|\bar d u\rangle ,
$$
for instance. But you may not superpose this on the neutral pion you started with:
As @Hyperon has commented, superselection rules prevent mixed charge superpositions: each charge sector lives in a "different world" so so speak. There are several questions illustrating this on this site. To the extent you are considering representations of conserved charge, you'll never have non-vanishing dot products of states of different charge. E.g., superselection sectors of different fermion number will stay apart, as fermion number cannot change.
An illustration: You'll presumably learn later on that S is violated by a bit (2nd order) by the weak interactions (box diagram), leading to, e.g. strangeness oscillations between $K^0=\bar s d$ and $\bar K^0= \bar s d$, at a frequency ~ 3.5μeV. That is to say, this neutral meson can transition to its antiparticle, so it does not form a leak-proof superselection sector! So you can, and do, form superpositions of indistinct strangeness, e.g.,
$$
K_L^0=\frac{1}{\sqrt 2} (|\bar s d\rangle -| \bar d s \rangle ) ,
$$
but distinct charge (still inviolable!). This is a propagating state, whose strangeness flip-flops in time, in collusion with $K_S^0$, its orthogonal combination. A formally analogous phenomenon occurs for neutrinos.
