Almost certainly not, unless you hold a valid CA Resale Certificate.
From the CDTFA: “Generally, nonprofit groups’ sales are taxable, as are their purchases. In other words, nonprofit and religious organizations, in general, are treated just like other California sellers and buyers for sales and use tax purposes.”
“Nonprofit organizations generally need a seller’s permit if they make sales of goods or merchandise in California. This is true even if the sales are not taxable.”
And “Although many nonprofit and religious organizations are exempt from federal and state income tax, there is no similar broad exemption from California sales and use tax.
Do you have a 503(c) letter from the IRS that says your organization is tax exempt?
An IRS letter cannot exempt you from State sales tax. IRS is federal government – has no jurisdiction over sales tax (which is from the CA Department of Tax and Fee Administration – CDTFA). A letter from the IRS saying they are a 503.c or similar is NOT a sales tax exemption. It is an income tax exemption. See above.