1. First, we're going to locate the mod files.
Go to your Steam library and right-click The Binding of Isaac: Rebirth from your games list. Then hover over "Manage" and then click "Browse local files" (like in the screenshot below).
https://i.imgur.com/6NlfW98.png
A file browser window should open, revealing the Isaac files. Open the folder "mods".

2. Now, we're going to open the Custom Stage API folder and this mod folder.
In "mods", you're going to open 2 folders:
https://i.imgur.com/eLpbdpP.png
https://i.imgur.com/6aseN3Y.png

3. We're going to replace the LIBERAL of Isaac files inside the Custom Stage API files now (don't worry, this is not dangerous and it will not affect Custom Stage API in any way)
Inside the LIBERAL of Isaac mod folder, you're going to inside a folder called "resources-dlc3", and you're going to find a file called "stages.xml".
Copy it and go to the Custom Stage API folder again, in which you're going to go inside the "resources" folder, and now you're going to paste the "stages.xml" file. If a windows appears saying "The destination has 1 file with the same name" click "Replace the files in the destination"

4. And you're done!
Have fun being a LIBERAL and doing WOKE stuff.