Rabbit skin glue to prevent mould on canvas

The quickest answer is the write, please do not do this. I will flesh this out a bit. First, animal skin glue is the most reactive material used in traditional and even modern paintings in terms of responses to changes in relative humidity. At low RH it is extremely brittle, at high RH it loses all film qualities and forces the paint to do all of the structural work. Old brittle paint can only crack.
One may ask if this is the case why are not all old paintings a mess? We to some extent the affect is mitigated by being trapped under a layers of paint/ground and that most of the time RH is not above 80% where real problems start. Other would say that today there is no real justification for using animal glue for sizing. I understand but am not totally on that side.
Animal glue on the back of the canvas would exacerbate any negative tendencies. Additionally, allpying animal glue onto the back of an already prepared and painted canvas could cause severe shrinkage to the support and possible loss of ground and paint layers. mold growth only occurs at high RH, the same ranges where animal glue starts to fail. In short, there is no good reason to do this.
In the past artists would sometimes size and prime both size of the canvas before painting. This could be done if desired, but I would suggest that the sizing be done on both sides before any priming or painting. Also, this would be best if done using an acrylic dispersion size and probably an acrylic dispersion ground if you do want to prime both sides.