Does Cyanoacrylate glue inhibit Mold Star silicone?

cyanoacrylate itself will not, however many brands of cyanoacrylate have additives which can.

Sulfur is your problem. P-silicon and sulfur do not mix.

I work primarily with fossils and use completely additive free cyanoacrylate, the downside it has to be used quickly as it has no stabilizers.

We don't use much platinum based silicon just becasue even trace amounts of sulfur in the fossils themselves can prevent it from setting up, but I have used to for artifacts. Likewise trace sulfur in the glue will also prevent it from setting. Any sulfur at all prevents P-silicon from setting up and many brands of cyanoacrylate glue use sulfur based stabilizers. many accelerator sprays also contain sulfur so don't use them if you can help it.

tin based silicon tends to be more chemically forgiving, but has greater shrinkage as it ages (months to years).

So you can switch silicon or find additive free cyanoacrylate.