If Luminous Blue Variables SDOR would be red - they would be SR LPV, but not eruptive 
It is not so straightforward.
Let’s see the SDOR definition in the VSX Variability types document:
Variables of the S Doradus type. These are eruptive, high-luminosity Bpec-Fpec stars showing irregular (sometimes cyclic) light changes with amplitudes in the range 1-7 mag. in V. They belong to the brightest blue stars of their parent galaxies.
As you see, they are not red variables because their spectral types are early. V0840 Cyg has a mean A3 spectral type.
As a rule, these stars are connected with diffuse nebulae and surrounded by expanding envelopes.
That makes them redder than what their spectral types imply.
Also known as LBV. The SDOR variability is known in the literature as an aspect of the LBV phenomenon, consisting of photospheric pulsations with time scales of hundreds to thousands of days and excursions to the redder part of the HR-diagram when the star is brighter (SDOR phases). Besides, they also display micro-variations, stochastic variability and eruptions.
Their spectral types change, and when they are brighter they are redder, but they are not semirregular variables, because SR stars do not show eruptions or such spectral behaviour. LBV stars are also more massive and luminous than the SR stars. The SR stars are mostly red giants, while most LBV stars are hypergiants.
Cheers,
Sebastian
Thank you, Sebastian, for important notes! Of course, the spectral difference is huge well as the processes. The LBV “saw” is noticeably sharper than LPV waves. I said just about first impression, no more
It may be interesting, that in GCVS LBVs belong to pulsating vars.