The wavefunction of superposed states doesn’t say anything about what the photon is ‘like’. It is a tool for letting you predict what you will measure. And what you will measure for a superposed state like this is that sometimes the measurement device registers a photon with a vertical polarization, and sometimes with a horizontal one. If the superposed state is described by a wavefunction that has an equal weighting of the vertical and horizontal wavefunctions, then 50% of your measurements will give the result ‘vertical’ and 50% will indicate ‘horizontal’. If you accept Bohr’s rigour/complacency (delete to taste), we don’t need to worry what the superposed state ‘is’ before making a measurement, but can just accept that such a state will sometimes give us one result and sometimes another, with a probability defined by the weightings of the superposed wavefunctions in the Schrödinger equation. It all adds up to a consistent picture.