Licorice root is not one ingredient. It is a plant extract containing dozens of compounds, and three of them do most of what skincare cares about.
Glabridin is the main brightening component. It slows tyrosinase, the enzyme that builds melanin, so less new pigment is made. It also has anti-inflammatory activity. Glabridin is found in the oil-soluble fraction of the root and is the compound most brightening claims rest on.
Liquiritin works differently. Rather than slowing pigment production, it appears to help disperse and break up pigment that is already there. It is water-soluble and shows up in different extracts than glabridin.
Licochalcone A is the anti-redness one. It comes from Chinese licorice, Glycyrrhiza inflata, rather than the classic species, and it is the compound in a number of well-known redness creams. It calms the inflammatory signaling behind flushing and reactive skin.
The practical problem is that "licorice root extract" on a label tells you which plant was used and nothing else. Two products with the same ingredient listed can contain completely different amounts of completely different compounds. When licorice works well in a product, it is usually because the formulator chose a standardized extract on purpose, not because the plant is on the list.
Topical licorice extract is among the gentlest things in skincare, and it is used specifically in products for people who react to everything.
Almost nobody needs to avoid topical licorice extract. It is mild and it is one of the standard ingredients in products aimed at reactive skin.
Avoid it if you have reacted to a licorice-containing product before, or if you have a known allergy to licorice or related plants.
Do not apply it to broken or weeping skin, which is true of any leave-on product.
Pregnancy and breastfeeding: topical licorice extract is generally considered fine, and it is one of the few brightening-adjacent ingredients most clinicians are relaxed about during pregnancy. Oral licorice is a different question - swallowing significant amounts of licorice in pregnancy is discouraged, and that has nothing to do with a face cream.
The realistic gate is what you expect from it. If you are buying licorice extract to clear melasma or long-standing dark spots, you will be disappointed, and something better exists.