Polarity and acid strength in alcohols
In analysing acid strength, bond polarity of the bond to the ionisable hydrogen atom is what should be considered, not the polarity of the molecule (i.e. the dipole moment). In the case of alcohols, the polarity of the $\ce {O-H}$ bond should be considered when assessing strength as an acid. 

Why does the bond dipole matter? In the process of ionisation $\ce {ROH + H2O-&gt; RO^{-} + H3O^{+}}$, the $\ce {O-H}$ bond is heterolytically cleaved. It is easy to observe that the greater the partial positive charge on the $\ce {H}$ atom, the more easy it is for it to be abstracted by the water molecule, due to stronger electrostatic attractions. Also, the more polar the bond, the lower the covalent character of the bond as the electron density shifts more towards the oxygen. Such a bond is also more easily cleaved. Recall that the covalent character of a covalent bond is highest when the atomic orbitals are of similar energies and that electron density is shared equally between the two atoms. 

In the primary alcohol, there is one electron-donating alkyl group attached to the alpha carbon while in the secondary alcohol, there are two such groups attached to the alpha carbon. Due to the greater electron donation to the oxygen atom in the secondary alcohol, where $\ce {R = CHR'R''}$ , the oxygen atom actually withdraws less electron density from the $\ce {O-H}$ bond. We can think of it this way: The oxygen atom has a fixed demand for electron density. When this demand is met by an increased supply from the alkyl chain, the demand for electron density from the hydrogen atom would decrease. Thus, the $\ce {O-H}$ bond is less polar and less easily heterolytically cleaved. 

Simarly, for the primary alcohol, where $\ce {R = CH2R'}$, there is also an increased supply of electron density from the alkyl chain R, as compared to $\ce {R = CH3}$. However, the increased supply from $\ce {R}$ is less so compared to that in the secondary alcohol. Thus, the primary alcohol would be a weaker acid than the methyl alcohol but a stronger acid than the secondary alcohol. 

Conventionally, acid strength is assessed using conjugate base stability, rather than bond polarity. A brief overview of assessing conjugate base stability can be found here.