So recently I have been trying to make my custom traits conflict with traits in game i.e. Hates Cats conflicts with Cat Lover. It works fine in CAS but once I leave it and return to the household the trait gets removed and I'm not sure why. I have attached the file so I hope someone can help!

The binary SimData file is used to indicate to the user interface how to manage traits. I can't read that file in the Sims4Data file editor, so I can't verify it is correct. I suspect the data file format has been updated and the program needs updating as well, but presumably you've tested the conflict in CAS and all is well in that regard.

The XML for the trait, however, is what is used once the Sim is loaded into the game, and this file has errors in it. It's always helpful when editing an XML file generated by the Mod Constructor (or whatever you're using) to format the XML in an indented fashion so these kinds of errors are less easy to introduce. I used the firstobject XML Editor to format the file in the indented style (hit the F8 key) and this makes it trivial to see that the conflicting_traits list is embedded inside a mangled display_name.

You'll need to reformat that mangled section as follows to allow the trait to be usable in the game: