  Galaxy clusters show a variety of intra-cluster medium properties at a fixed
mass, among which gas fractions, X-ray luminosity and X-ray surface brightness.
In this work we investigate whether the yet-undetermined cause producing
clusters of X-ray low surface brightness also affects galaxy properties, namely
richness, richness concentration, width and location of the red sequence,
colour, luminosity, and dominance of the brightest cluster galaxy. We use
SDSS-DR12 photometry and our analysis factors out the mass dependency to derive
trends at fixed cluster mass. Clusters of low surface brightness for their mass
have cluster richness in spite of their group-like luminosity. Gas-poor, low
X-ray surface brightness, X-ray faint clusters for their mass, display 25\%
lower richness for their mass at $4.4\sigma$ level. Therefore, richness and
quantities depending on gas, such as gas fraction, $M_{gas}$, and X-ray surface
brightness, are covariant at fixed halo mass. In particular, we do not confirm
the hint of an anti-correlation of hot and cold baryons at fixed mass put forth
in literature. All the remaining optical properties show no covariance at fixed
mass, within the sensitivities allowed by our data and sample size. We conclude
that X-ray and optical properties are disjoint, the optical properties not
showing signatures of those processes involving gas content, apart from the
richness-mass scaling relation. The covariance between X-ray surface brightness
and richness is useful for an effective X-ray follow-up of low surface
brightness clusters because it allows us to pre-select clusters using optical
data of survey quality and prevent expensive X-ray observations.
