According to the USDA Food Service, Accommodating Children with Special Dietary Needs in the School Nutrition Program, while schools are required to make accommodations per the ADA (Americans with Disabilities Act) and the IDEA (Individuals with Disabilities Education Act):
Generally, children with food allergies or intolerances do not have a
disability as defined under either Section 504 of the Rehabilitation
Act or Part B of IDEA, and the school food service may, but is not
required to, make food substitutions for them.
However, when in the licensed physician's assessment, food allergies
may result in severe, life-threatening (anaphylactic) reactions, the
child's condition would meet the definition of "disability," and the
substitutions prescribed by the licensed physician must be made.
Your particular provider may not be explicitly bound by these regulations (depending on if they participate in an USDA program or not), but likely the same basic guidelines do have some impact - the ADA would at minimum apply. Essentially, they probably do not have to make an accommodation.
I would recommend that if you are concerned about this, you look into your state's requirements in more detail; someone at the Pennsylvania DHS may be of some assistance. The Pennsylvania Code (law) related to this can be found here, search for "Food". It's not very specific, other than requiring allergen lists be kept, unfortunately, so likely there are no regulations that will help you here. My state (Illinois) is a bit more specific in their regulations, but they still would permit the daycare to do this (although the wording seems to allow for some argument here, as the daycare must prove that it would cause undue hardship for them to meet these regulations).
I would guess that the particular reason for this change was that the daycare center failed an audit (either internal or external) in regards to its correct separation of utensils when preparing food. For example, with meat-allergic children in the center they likely would need to keep two separate sets of dishes - one for cooking meat, one for cooking things the meat-allergic children could eat. Just washing a dish may not be sufficient to prevent allergens from remaining. It's likely that they were not doing this before, and while your child's meat allergy may not be so severe for this to be a concern, laws and regulations tend to assume worst case scenarios.
As such, it's not surprising to me that they'd require you to bring all meals (including vegetarian) into the center. I would certainly recommend trying to negotiate a discount for this, and if they're unwilling (or it's too much of a burden to you to bring your own food) consider finding another center that is more capable of serving your children's needs; larger centers may be more able to handle the specific needs of your children due to volume, or even smaller (at-home type) centers may be more willing to change as well. You also may be able to find a vegetarian-friendly center, as that is becoming more common.