If i captive breed garden snails do they still carry parasites?
Outside United States
I presume that the specific concern are parasites that can also affect humans.
These parasites have complex life cycles that involve at least one vertebrate, usually a rodent, to be complete. Therefore, if you can culture your snails in a manner that prevents them from contact with rodent feces then it is very probable that these will be parasite free.
However, since you are writing from outside Colorado I suggest you locate local sources of information regarding the specific parasites that are present that involve snails as intermediate hosts, and to determine the life cycle of these parasites.
Once you have done that, and modified your culture to prevent completion of the parasite life cycle, you should be fine.