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I managed to fix my problem after looking through all the other possible settings I could fiddle with. I had to clear the settings and data specifically for Derpibooru rather than clearing cookies in general. If anyone runs into a similar problem, specifically for chrome, here's what I did.
1. Go to settings
2. Go to site settings
3. Go to all sites
4. Search for Derpibooru
5. Tap and clear settings and data for each instance of Derpibooru.
After that it should work. If for whatever reason Chrome isn't responding while going through any of the steps, choose wait rather than closing the app. Tap whatever selection you're going for every now and then. Eventually Chrome will respond.
1. Go to settings
2. Go to site settings
3. Go to all sites
4. Search for Derpibooru
5. Tap and clear settings and data for each instance of Derpibooru.
After that it should work. If for whatever reason Chrome isn't responding while going through any of the steps, choose wait rather than closing the app. Tap whatever selection you're going for every now and then. Eventually Chrome will respond.