I had the exact same problem and went to plugins > buddypress > bp-xprofile > bp-xprofile-filters.php and had a look. At the very top there is a very nice list of filters, all of them starting of “add_filter”. When you want to remove something WITHOUT touching the core, simply find the one you want, copy and paste it into your functions.php inside your theme, and then replace “add_filter” with “remove_filter”.
In this case just replace what you had before with the code below and it should work: