This code snippet for WooCommerce Subscriptions will only allow a single purchased subscription across all subscription products for customers.

wc-subscriptions-only-allow-one-subscription.php

add_filter('woocommerce_add_to_cart_validation', 'check_num_of_subscriptions', 10, 2);
 
function check_num_of_subscriptions( $valid, $product_id )
{
    $product_to_add = wc_get_product( $product_id );

    if ( $product_to_add instanceof WC_Product_Subscription || $product_to_add instanceof WC_Product_Variable_Subscription) {

        // alternative use: $has_sub = wcs_user_has_subscription( '', '', 'active' );
        if ( has_active_subscription() ) {
            // cart validation must fail, because user is not allowed to have multiple subscriptions

            wc_clear_notices();
            wc_add_notice(__('You already have an active subscription.', 'woocommerce'), 'error');
            return false;
        } else {
            return true;
        }
    }
    return $valid;
}

function has_active_subscription()
{

    $user_id = get_current_user_id();

    $active_subscriptions = get_posts(array(
        'numberposts' => -1,
        'meta_key' => '_customer_user',
        'meta_value' => $user_id,
        'post_type' => 'shop_subscription',
        'post_status' => 'wc-active'

    ));
    if (!empty($active_subscriptions))
        return true;
    else
        return false;
}

there is an issue with this code, if the user has the subscription already, the user cannot upgrade or downgrade. its blocks everything

add_filter('woocommerce_add_to_cart_validation', 'check_num_of_subscriptions', 10, 2);

function check_num_of_subscriptions( $valid, $product_id ){
    $product_to_add = wc_get_product( $product_id );
    if ($product_to_add instanceof WC_Product_Subscription || $product_to_add instanceof WC_Product_Variable_Subscription){
                // alternative use: $has_sub = wcs_user_has_subscription( '', '', 'active' );
                
                if ( has_active_subscription() && (! has_woocommerce_subscription('',$product_id,''))) {
                    // cart validation must fail, because user is not allowed to have multiple subscriptions
                    wc_clear_notices();
                    wc_add_notice(__('You already have an active subscription.', 'woocommerce'), 'error');
                    return false;
                } else{
                    return true;
                }
     }
    return $valid;
}
function has_active_subscription(){
    $user_id = get_current_user_id();
    $active_subscriptions = get_posts(array(
        'numberposts' => -1,
        'meta_key' => '_customer_user',
        'meta_value' => $user_id,
        'post_type' => 'shop_subscription',
        'post_status' => 'wc-active'

    ));
    if (!empty($active_subscriptions))
        return true;
    else
        return false;
}

function has_woocommerce_subscription($the_user_id, $the_product_id, $the_status) {
	$current_user = wp_get_current_user();
	if (empty($the_user_id)) {
		$the_user_id = $current_user->ID;
	}
	if (WC_Subscriptions_Manager::user_has_subscription( $the_user_id, $the_product_id, $the_status)) {
		return true;
	}
}