Why is the wavefunction of a mixed-flavor baryon (e.g. the proton) antisimmetric under exchange of quarks of different flavors?

A similar question has been put before in this forum, but not with full clarity. So I would like to revisit the question and express it differently, hoping for a crystal clear answer.

The question is: why should hadrons made up of different flavours of quarks have to be antisymmetric with respect to the exchange of all quarks involved? An example is the proton (with uud quark content). Let me clarify why this puzzles me.

1. If I could treat flavours as labels for physical states of a single particle, the way spin components and spatial positions are, then everything would make sense. But it doesn’t seem to me that I can think of flavours as states. Indeed,
2. Spin components are labels for a physical state, on account of rotational invariance: specifically an observer could re-orient his or her axis (a conventional choice) and a spin up quark would appear as a spin down quark. Similarly for positions and momenta: a translation or a boost of the laboratory system would change the position or momentum labels. So I am justified in thinking of spin and positions as labels for states of the same object. Similarly,
3. The degrees of freedom of exact internal symmetries (say colour SU(3)) are also labels. In this case, they are labels for different redundant descriptions of the same fundamental physics. So for instance, a green quark will become a blue quark under a local colour SU(3) gauge transformation, a conventional choice. Again I am justified in thinking of colour as labels for states of the same object
4. But when it comes to flavour, the "symmetry" is at best an approximate symmetry of a portion of the Lagrangian (the strong interaction), and we can positively distinguish different flavours through electric charge, mass and other effects of non strong interactions. So how can I be justified in thinking of them as labels for the same object? And if they are not, why should I impose antisymmetry among distinguishable objects?

One more consideration,

• The flavour symmetry. although approximate, has at least one implication, the existence of hadron multiplets with similar masses, identical spins and so on. This is because the mass is dominated by the symmetric strong force. Now, if one hadron in a given multiplet is antisymmetric under exchange of the constituent quarks, then so must be all others, since the flavour symmetry commutes with particle exchange. So for instance, $Delta^{++}$ (quark content uuu) must be antisymmetric under quark exchange since all quarks are identical, and that implies that the same is true for $Delta^{+}$ (quark content uud), since it’s in the same multiplet.
• But when it comes to protons and neutrons, there are no hadrons in their multiplet (both SU(2) and SU(3) multiplets) with all quarks having the same flavour, so this line of reasoning doesn’t seem to help either.

So what gives? Am I thinking about this wrongly? Please note that my point of contention is that I don’t buy flavours are labels for states of a single object (a "quark"). If you think they are, could you address my objections?

Many thanks