How did you add the field to your CRED form? Can you show me where you insert the field?
As a quick test, try auto-generating the form and seeing if it is output correctly, and compare how the field is inserted then with what you have done. (If you don't want to change your current form you can make a second form purely for testing where the markup is auto-generated.)
I followed your link to the auto-generated form and I was confused for a while because it looked like it was working, but then I realised you have a checkbox custom field location and a checkbox taxonomy location, and the custom field is working correctly and the taxonomy not, yes?
I set up a test site locally to test the same scenario and I found it didn't work, much like in your case.
I'm going to escalate this as a bug, but in the meantime I suggest you try renaming the slug of your taxonomy, even a small change such as to "locations". Then edit your post form to change the field slugs for the taxonomy to match.
I've been going through the history - there are quite a few people that have modified functions.php to do this - I'm comfortable with php but want to make sure I'm modifying the correct functions.php file.
Is this the functions.php:
wp-content > plugins > cred-frontend-editor > application
or do you mean the theme functions?
You would edit the theme's functions.php, never the plugin files, and you might find it easier to use a plugin such as Code Snippets to add your PHP, in which case were you to ever change theme your code would be preserved.
The first code in that thread you linked to is what you require, with suitable edits for the id of the cred form and the slug of the taxonomy.
I don't know without checking, so why don't I tell you how to check so that you can work this kind of thing out for yourself in the future if you have related questions.
To know what field name or slug is being used, dump $fields to your debug log so that you can see the fields submitted with the form and how to access them.
So once $field_data has been split into $fields and $errors you can use error_log( $fields ); to print it to the debug.log to inspect it.
To make complex variables ($fields is an array) more readable, use it like this:
error_log(print_r( $fields, true ));
If you haven't already, turn on the debug log by editing your wp-config.php file and change the line with WP_DEBUG like so: