You can control who can raise feedback/feature request in Salesforce via the purple question mark. You can select both on which objects is the feature available as well as which groups of users are allowed to leave feedback.
To manage feedback availability you will need:
Enterprise, Unlimited or Consulting Plan
Choose objects where feedback is available
When you open the Org model, from the top-level node, select the 'feedback' tab. Click on the text button to open org-wide settings. Here you can:
Turn off feedback on all objects
Turn on feedback on all objects
Search for specific objects and turn on feedback individually
Click on the pencil icon next to the object to open feedback settings for that object
Choose audiences that can leave feedback
In the right panel for a given object, in the feedback tab, use the group field to add or remove groups of users that will be able to see and leave feedback on the objects, its record types and fields.
By default, 'All' users can leave feedback. Remove that group and add your custom groups by typing and selecting the desired group from the dropdown.
Report on feedback settings
You can run a report on feedback settings to quickly check which objects have enabled feedback and what user groups can raise it for each object.
Managing feedback availability by both objects and audiences allows you to tailor the usage of this capability to different needs:
You can enable feedback on new objects (for instance, when you install a new package or build a new application) to collect early feedback from end users and disable it once the capability settles.
You can give each team ability to leave feedback on their objects (e.g. sales team being able to leave feedback on opportunities, marketing being able to leave feedback on campaigns etc.) all the time to support a continuous improvement program.
In large organizations, where you might be worried about being overrun by incoming requests, you can delegate this right to managers or a specific subset of users who speak on behalf of their teams.