Can I be sued for cutting someone out of a project when no contract was ever signed?

Oral contracts are enforceable in CA, although they're harder to prove than written ones, and email, texts, and witness testimony can all be used to prove the terms of an oral contract and its breach. So you can be sued by this person for breach of an oral contract to co-produce the film, and they may also claim that they contributed to the development of the concept, and are entitled to co-authorship credit and compensation.

It sounds like the emails will support a claim that this person was working on this project, and you had a deal to share the project with them. Whether they can prove that they had a deal specific enough for a court to enforce, especially since you state that you didn't agree on what rights or percentage they'd get, remains to be seen. You may also be able to establish that their services were contingent on finding financing. if however, this person spent a lot of time on this project, and made their expectation of receiving credit and compensation known to you, and did perform producing services and accomplish producing tasks like contacting or attaching talent and crew, creating a budget, scouting locations, making financing connections, etc., they may have a good argument that they're entitled to producer credit and compensation.

Consult an entertainment lawyer to fully disclose the facts of your situation and get some specific advice.

Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.