Inline style fetched from database I'm editing an existing Drupal 7 site, with coloured menu buttons, and each part of the site has the corresponding colours in it's titles and links.
For example: the menu item "about us" is coloured orange, and each subpage of "about us" uses orange for it's titles and links.

The problem is: these are all inline styles, fetched from the database table "field_data_field_colour" and printed by a template.
I can change the hex-colour values directly in the database, but I've looked everywhere and can't find where to change/set those colours without messing with the database.
The pattern field_data_field_ refers to Field storage. This data is attached to an entity of some kind, most likely a Node. You can learn more about content management on drupal.org, Nodes, content types and fields.

You should edit the node that you want to modify (admin/content or click Edit on a node if the tab hasn't been styled out of existence), and find the field that someone added there. Then you can change the value. You can check what fields are used in which entity types by going to /admin/reports/fields. Each field usage has a link to its respective Field Management page where you can learn more about how that particular field is configured.

Modifying field_data_field_ directly in the database is incorrect because data retrieval happens in field_revision_field_ tables.