First, I do not have any idea how the particular volunteer fire department you're referencing is organized. California laws regarding VFDs are scattered among several codes. None of them seems to say anything other than "regularly organized," whatever that means. So, I'm going to presume that some VFDs are organized as nonprofit public benefit corporations (NPBCs) under Corporations Code sections 5110 through 6910. Maybe a lot of them are.

Next, NPBCs would have the right to fund-raise by bake sales and similar activities, but not to imply that donations to them are tax-exempt. Being "nonprofit" and being "tax exempt" are different concepts. A NPBC is nonprofit by definition, but tax exemption requires that the organization take another step, and that is to obtain that status from the Internal Revenue Service and become qualified under the Internal Revenue Code, probably under IRC section 501(c)(3) or 501(c)(4). This can be a difficult step - much harder to accomplish than forming the NPBC in the first place - and probably many VFDs do not attempt it.

Finally, your selection of the phrase "use the funds for whatever they want" is troublesome. Any organization raising funds needs to tell the contributor with reasonable accuracy the intended use of the funds, whether it be a private business corporation selling stock, or the Little Sisters of Charity raising money to house, clothe and feed orphans. I doubt that a VFD would be justified in raising funds in its name that were ultimately to be used for the personal benefit of volunteer members of the department, if that's what you mean.