Hi,
Because the instance CSS file is dynamically generated depending on the search options, on multisite networks, this is automatically stored in the upload path, which is shared across the network.
You could turn on this option here: https://i.imgur.com/wFWJZ3z.png
This will print the stlyes directly to the head as inline styles, bypassing this dynamic CSS file.
I could also suggest a modification, that would automatically try to load the instances CSS file from the current domain, but it may run into a non-existent file issue, as this file may only exist on the main domain upload path.
If I may, CSS files should not be a concern of GDPR regulations, as those are only statically served cascading stylesheet files – should not capable of collecting any information about the user. (unless there is some sort of hacky way of servers file access logging, but those are usually exceptions)