I’ve heard that allergy drops are not approved by the FDA. Is that safe?

The FDA approves products, not therapies, so it’s unlikely that it will ever “approve” custom, multi-antigen sublingual immunotherapy.
Antigens are labeled by the FDA for single use through injections and some for sublingual immunotherapy. Multiple antigen therapies for both injection and sublingual use are an off-label use of FDA-approved biologics.
Most physicians prescribe FDA-approved drugs in an off-label manner today, for example, the use of blood pressure medications for migraines, montelukasts for COPD, or arthritis drugs to treat shingles.