Filter to use the Basic User Avatar on the BuddyPress Profile.

my_bua_bp_avatar.php

<?php
/**
 * Filter to use the Basic User Avatar on the BuddyPress Profile.
 */
function my_bua_bp_avatar( $image, $params  ) {
	// Determine if user has a local avatar
	$local_avatar = get_user_meta( $params['item_id'], 'basic_user_avatar', true );

	if ( empty( $local_avatar ) ) {
		return $image;
	}

	if ( ! empty( $local_avatar ) ) {
		$thumb_src = $local_avatar['128'];
		$bua_img = sprintf( '<img src="%s" width="%d" height="%d" alt="%s" class="%s" />', esc_url( $thumb_src ), absint( $params[ 'width' ] ), absint( $params[ 'height' ] ), esc_attr( $params[ 'alt' ] ), esc_attr( $params[ 'class' ] ) );
		return $bua_img;
	}

	return $image;
}
add_filter( 'bp_core_fetch_avatar', 'my_bua_bp_avatar', 10, 2 );