Having to pass the FE exam is universal. The requirements to obtain your EIT varies depending on what state you decide to apply in. Generally speaking, if a state licensing board requires that you had previously passed the FE exam or obtained an EIT certificate, they will accept the EIT regardless of where you obtained it as long as the originating board verifies that you obtained it by passing the FE.
California accepts an EIT from other states when the applicant is applying for PE licensure.
One thing to watch out for...some employers only allow for EIT from the state in which the employer is located as a condition of employment. City of Los Angeles is one of those employers that will not recognize an EIT from any where else but California. The Board has explained the situation many times in the past, but their personnel department refuses to acknowledge the fact that an EIT gained anywhere is equivalent to obtaining it in California. Now, California Board offers Comity EIT certificates to those individuals that need this as a condition of employment. Apply just like everyone else and ask for Comity status by providing a verification form from the originating state and the Board will send you a new certificate.