Automatically approve membership requests that satisfy some criteria.

auto-approve-some-bp-membership-requests.php

<?php 
/**
 * If a user submits a site membership request, but has a
 * 'my-school.edu' email address, bypass the manual approval of the request.
 *
 * @param bool  $send    Whether or not this membership request should be approved
 *                       immediately and the activation email sent.
 *                       Default is `false` meaning that the request should be
 *                       manually approved by a site admin.
 * @param array $details The details of the request.
 */
function bpcodex_auto_approve_some_requests( $send, $details ) {
	// We'll need the prospective user's email address.
	if ( empty( $details['user_email'] ) ) {
		return $send;
	}

	$email_parts = explode( '@', $details['user_email'] );

	// If the email address is one of ours, approve the request.
	if ( ! empty( $email_parts[1] ) && 'my-school.edu' === $email_parts[1] ) {
		$send = true;
	}

	return $send;
}
add_filter( 'bp_members_membership_requests_bypass_manual_approval', 'bpcodex_auto_approve_some_requests', 10, 2 );