Is it possible to prevent certain values from being stored in the Pulumi State file? (For example, RDS Passwords and K8S Secrets). I don't need to track changes to these values - it is possible to tell Pulumi to using a value while provisioning and then discard?

Not currently, but we have work in progress right now on features to enable this - which we’re expecting to be available in the next couple weeks. Properties that are marked as secret (whether from config or from outputs of other resources) will be stored in encrypted form in the checkpoint. See https://github.com/pulumi/pulumi/issues/397.