I have current as well and older MSDS on Break-Free CLP as my job and shop used it frequently in large quantities over many years.
Going back to 1989 a "possible" carcinogen was identified in the formula and it was changed. .
The current formula is pretty harmless except as with all petroleum, especially synthetic petroleum products, repeated use and saturation can cause de-fatting of the tissue so washing your hands after use is the way to go.
Directly from BF's MSDS:
EMERGENCY OVERVIEW
While expected to be non-irritating to skin, eyes and by ingestion, as with all petroleum products, prolonged and repeated contact with
skin could cause irritation and possible dermatitis. The synthetic oils and additives could also be absorbed through abraided skin, but
results of dermal toxicity tests suggest that no acute systemic effects would be experienced by healthy individuals.
SKIN:
Possible slight to moderate redness may occur with extended daily exposure. Product is not classed as a primary skin irritant or corrosive.
So basically don't bathe in it, wash your hands and you'll be fine. Anyone who works as a mechanic would have far more exposure to the possible negative effects from coming in contact with grease.
If you want to read something truly scary, read an MSDS of some of the household cleaner's and you'll never want to touch the stuff again.