The short answer to your questions is that an actual driver's license is not required to be a lawful member of a medical cannabis collective. Pursuant to the CUA, the MMP, People v. Colvin, and People v. Jackson, all that is required to be a member of a collective is 1) that you are a qualified patient, 2) associated with other qualified patients to collectively or cooperatively cultivate and distribute medical cannabis, and 3) not for profit.
However, each collective can maintain their own rules pertaining to admission and standing within the association. The issue that you are running into is that the collective dispensary that you are attempting to enter is requiring you to present a drivers license. The reason for this is probably to both verify your identity as well as your status as a California resident. These same basis are why most collective dispensaries will probably have a similar requirement.
Functionally, I don't see much of a privacy benefit to you in utilizing a passport card rather than a California Driver's License of I.D. card. You also probably won't get very far arguing with the dispensary operators to grant you admission outside of their general policies. This means that your practical consideration is whether to acquiesce to their demands of having a California ID or find another means of obtaining your medicine regardless of what either the CUA or MMP actually state.
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If you don't want a driver's license, you can get a California ID card issued by the DMV.
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The medical marijuana laws do not require you to have a California ID to use marijuana, but they also do not prohibit a dispensary for asking for one to join their group or use their products.
Check the link below, maybe you will be able to find a dispensary that will accept the passport.