Air can get in a system when servicing (replacing) components.
With respect to compressibility, introduced air bubbles was not
the characteristic I was referring to.
If air is entrapped in the system (bubbles) this will of course be noticible when the brakes are pushed hard because air is far more compressible than hydraulic fluid.
It appears that the reason silicone based fluids are more compressible relates to the density of the fluid. Further, that the dimethyl polysiloxane contains significantly more disolved air than glycol ether based fluids. This is air between the molecules and does not effect volume.
This dissolved air is not something to generally be concerned about. The problems for racers
is twofold. First, they tend to be very sensitive to changes in pedal feel and vehicle response. Second, the brake fluid can get hot, very hot. The silicone fluids get noticibly more compressible as the temperature rises. This is disconcerting to say the least.
For making a decision about whether this may be a concern here's something to consider. If the pads and shoes aren't getting that hot, then the brake fluid isnt going be very hot. So the first question is whether the car will be in situations that require linings for higher temperatures and/or use up pads each event.ref.
Air solubility information comes SAE J1705, Appendix A, A.2.2.8 which was quoted in two unrelated sources. One a manufacturer's promotional paper The ABCs of Brake Fluid
and the other in appendix A of a 1992 US Army investigation Purdy, Ellen Report 2505 (pdf)
The practical effect of compressibility is covered in the army report but does not cover situations where the fluid temperatures get elevated. A 1981 SAE paper given by G W Holbrook has been referenced for testing that showed that gycol fluids compressed less than .3% from 77 to 250 degrees F. Whereas silicone fluid compressed .85% at 77 F and had almost doubled that to 1.54% at 250 F.
At 400 degrees, the silicone compressed 2.41% while the glycol was around 0.5% A couple of important points here. If the glycol based fluid is old, it will have absorbed moisture and its boiling point could be under 400 F. Second is that depending on the braking system, the compressibility may be noticible not just in feel but in pedal motion. Holbrook reported additional 1/2" of pedal movement at 400 F. The reporter (who clearly prefers DOT5) calculated increased pedal movement for his triumph at different conditions. He came up with very just 1/10" with new pads at 150 F, to 0.4" with worn pads when at 440F.
One thing every source seems to agree on is not to mix the two types of fluid!