For an employer, possibly.For nursing school
, it prevent you from attending.
The issue has less to do with the school and much much more to do with clinical sites and experiences.
attend clinicals at several hospitals. The requirements vary greatly and students must fulfill all reasonable ones. As the hospital takes a great deal of risk to permit students there, most receive no recompense for having students, and students add significant work to staff, most sites feel justified in requiring students to meet their Health standards, and no reason to bend them.
Also some depts are more restrictive with requiring vaccines such as oncology, ICU, pediatrics or neonatal. As a student, you must receive training all areas or not pass. If your school cannot get a site that will accept you, adios nursing degree.
Some will allow DOCUMENTED allergy/health exceptions, a very few, religious exemptions.
If your lack of flu vaccination has to do with scientifically unsubstantiated theories, you may not be able to obtain exemption. With most schools pushing evidence based research, and many sue happy lawyers, few places will want to take the risk.