All nudges in the Marygold app are triggered by events. For example if you create a date nudge then a notification will be generated when the date-conditions are met (e.g. the 1st of the month).
All other nudges (other than date nudges) either use a trigger event based on the account balance in one (or many) external accounts, or need access to your external account to sum receipts. For example a tax reserve nudge might be triggered by a date, but cannot calculate your suggested reserve contribution without being able to sum your receipts..
So if you don't consent to linking external accounts, these other types of nudge simply cannot work.
But it is totally up to you whether you want to use these features or not. The Marygold app does not need you to link any external accounts to work.