Schools that use federal funds are legally required to offer services to support students with disabilities.
Private schools are not.
That means that public schools and charter schools must give support services to those who qualify. Some private and faith-based schools will offer this support, but they are not required to do so.
NOTE: Private schools must still comply with the Americans with Disabilities Act and they must provide accommodations if their students have 504 plans.
Here's what you can do:
If you're choosing a school for your child, find out about how the school deals with special education services. Talk to other parents.
If you're considering a private or faith-based school, make sure they are willing to give your child what they need. Know that you do not have the law to back you up in this case.
Look into the School Choice Program. This is a program to help families of kids with disabilities to pay for certain non-public schools that can serve their child's needs.
This gets confusing! You do have some rights, even in a private school. Talk with your school district to learn more.
Source: LA DOE