Updated: Oct 4
Short answer: they shouldn't be. Long answer: it depends on the lash artist you decide to visit.
Lash extensions are synthetic fibers applied to the natural lashes using a cyanoacrylate-based adhesive — a strong chemical that allows for retention (the amount of time the bond lasts) of up to eight weeks. While this doesn't sound like it would the best thing to put on your face — it is glue, after all — if it's applied by an experienced lash professional who prioritizes the health of her clients and her clients' lashes, it does no harm. Not to the lashes, not to the lids, and not to the eyes in general. Let's talk about why.
The adhesive bond between extension and natural lash never touches the skin. It is your lash artist's job to ensure that she is getting as close to the base of the natural lash as possible without making contact with the actual eyelid. Adhering the extension to the very base of the hair follicle where it touches skin will suppress the growth cycle of the individual lash it is on, as the adhesive essentially glues the pore shut and does not allow the hair to grow or shed healthily.
The state and health of the client's natural lashes are carefully considered during the lash mapping process. An experienced lash artist who cares about the health of her client will ensure that she is choosing only the diameters and lengths that the client's natural lashes can comfortably hold. Some lash-lines can take a lot more than others and it is the lash artist's responsibility to ensure that she's accurately gauging how much each client can take, as it is possible to overweigh the lashes and cause discomfort, pain, or breakage/damage.
Lash extensions are placed on one individual lash at a time. A good quality set of lash extensions should be done with proper isolation so that bases don't become glued together. Placing a lash extension on lashes that have not been properly isolated significantly increases the risk of damage to the natural lashes.
Long story short, go to a licensed and experienced professional! Do not put the health of your lashes at risk by going to someone who prioritizes money over their clients.