Because these kits are intended for home use, there is generally a very wide safety margin, assuming you follow the instructions of the peel. But the trade-off for increased safety is decreased effectiveness, at least in the example of chemical peels. Chemical peels work by damaging the outer layer of skin; the deeper the damage, the more dramatic the result. So although a home chemical peel is likely to be very safe, it will also result in minimal improvement.
Medical-grade chemical peels are administered in a physician’s office, and thus are stronger and more effective than the over-the-counter version. In addition, I always recommend a skin care evaluation, which many offices offer for free. You may be using a chemical peel to treat a problem for which there is a more-effective treatment. One great example of this is hyperpigmentation; although chemical peels will very gradually improve pigmentation, a BBL laser treatment is much more effective.