Why is there an official census if the unofficial results are known?
The short answer is that the unofficial results are most probably fairly inaccurate and also lack the authorization and active participation from the player factions. Why are the results inaccurate? The data of various systems of the listed factions does not reflect a consistent state at a single date, or rather a single tick of the Background Simulation of Elite Dangerous (BGS). In extreme cases months could have elapsed between two system submissions to the EDDB that are summed up in a single unofficial census evaluation. Not only the influence values might change in these periods but also system control and faction presence.
How should I obtain consent of my player minor faction for entering the census?
The short answer is according to the customs or regulations of your player minor faction. If you have a procedure for faction decisions regulated, please follow that procedure. If your usual way to make decisions about your faction is to make a vote, notification, raise a question, or something else, please do that. If you are an appointed leader with authorization to make such decisions, then you're welcome to submit the entry on your own. Please note that the census organizers have no means to check whether these customs/regulations were followed and are not liable for any entries.
How should a sample be be submitted to provide consistent data?
If you submit your data via EDDB you need to make sure to update the data of all the systems your faction is present in within a single tick. The easiest way to do that is to launch ED Market Connector (EDMC) or another program that feeds Elite Dangerous Commanders Log system data to EDDB (EDDN) and hyperjump to each systems your faction is present in within a single tick (15:45 UTC to 15:15 UTC the next day) and before EDDB API is updated (04:00 AM, second day: see next question). You can check whether all your presence systems are in EDDB and are updated in the Minor Factions page of EDDB by entering your faction's name to the "Jump to a minor faction" field, clicking the "Find Minor Faction" button and scrolling through your faction's systems checking the update times in the end of each systems' headers.