Yes, the yellow fever vaccine appears to be safe for people with an egg allergy. A recent study in Brazil on children who have differing levels of egg allergies showed the yellow fever vaccine to be generally safe for people with an egg allergy, presumably because of how little actual egg material is present in the vaccine.
The role of eggs in manufacturing the yellow fever vaccine
An interesting fact is that the yellow fever vaccine commonly used around the world is cultivated in chicken eggs. This is actually a very common way to produce vaccines and it is how flu vaccines are generally produced. The virus has to have some place to grow and reproduce, and the current yellow fever vaccine uses the actual virus, in its weakened form. The chicken eggs are not a necessary vaccine component but it is highly likely that some of the material from the eggs can end up in the vaccine due to the way the virus was propagated.
The egg allergy and yellow fever vaccine study
Lopez and colleagues (2023) followed the yellow fever vaccination of 435 children, 225 (51.72%) of whom were classified as probably allergic to egg protein. Of the 435 children who received the yellow fever vaccine, 95.2% experienced no vaccine reaction. Most of the children who did react to the vaccine showed only mild skin rash. Only one child experienced a severe vaccine reaction (possible anaphylaxis). This is evidence that the yellow fever vaccine is safe, even for people with an egg allergy. In this study, only one out of 225 children who presumably had an egg allergy actually had an anaphylactic reaction (or something akin to it). The rest were fine.
Conclusion
Yes, the yellow fever vaccine does appear to be safe for people with egg allergies. If you have an egg allergy be sure to let your vaccine provider know about it so that they can monitor you for anaphylaxis reactions after you get the vaccine.
References
Lopes, F. T. T., de Castro Romanelli, R. M., de Oliveira, L. I., Abrantes, M. M., & Rocha, W. (2023). Safe Administration of Yellow Fever Vaccine in Patients with Suspected Egg Allergy. Journal of Allergy and Clinical Immunology: Global, 100089.