Hi Dave,
Welcome to BuddyDev.

Thank you for the question.

BuddyPress does not allow upload to avoid security issues. this is feasible to allow users upload media but not recommended.

To enable uploading for any user, you need to enable upload button and gran user upload_files permission

// grant all users upload permission.
add_filter( 'user_has_cap', function ( $all_caps, $caps, $args, $user ) {

	if ( 'upload_files' !== $args[0] ) {
		return $all_caps;
	}

	if ( is_user_logged_in() ) {
		// grant all needed caps.
		foreach ( $caps as $cap ) {
			$all_caps[ $cap ] = true;
		}
	}

	return $all_caps;
}, 10, 4 );

// enable upload button in text area.
add_filter( 'bp_xprofile_field_type_textarea_editor_args', function ( $args ){
	$args['media_buttons'] = true;

	return $args;
});

That will allow any logged user to upload images/other file types.

Please do note that this is not recommended as it may be a security nightmare to allow everyone uploading.

Regards
Brajesh

You are welcome.

I am sorry, I am not aware of any existing solution for BuddyPress xprofile that allows this.

Regards
Brajesh