I *believe* CaF2 does not etch appreciably in HF, as I've seen that CaF2 windows/optics have been used as carriers for Sirtl etching (HF + CrO3) with success by Eg. Shamsul Arafin, TU Munich (in his dissertation).
CaF2 will not dissolve in aqueous HF. For HF burns a 2.5% calcium gluconate gel is applied to neutralize HF (via the formation of CaF2). That provides good evidence for the insolubility of CaF2 in aqueous HF.