Clear Body/White Smoke does not prevent stat stages being directly modified by Heart Swap, Guard Swap, Power Swap, Baton Pass, or Topsy-Turvy. It does not prevent Spectral Thief from stealing (i.e., resetting) positive stat changes.
So Heart Swap, Guard Swap, Power Swap and Topsy-Turvy can lower stat stages, while Spectral Thief can still steal stat stages
Clear Body/White smoke also do not stop Self-inflicted stat lowering (like from Superpower) or Pokemon with Mold Breaker/Teravolt/Turboblaze lowering your stats.
Source 1
Source 2