Ah, I'm so dumb. I added new lines after all of my XML tags for readability, but they're interfering with how ActiveMerchant parses and evaluates the response.
So the correct XML response mock would be:
HTTP/1.1 200 OK
Content-Type: text/xml; charset=utf-8
<?xml version="1.0" encoding="utf-8"?>
<createCustomerProfileResponse xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xmlns:xsd='http://www.w3.org/2001/XMLSchema' xmlns='AnetApi/xml/v1/schema/AnetApiSchema.xsd'>
<messages>
<resultCode>Ok</resultCode>
<message>
<code>I00001</code>
<text>Successful.</text>
</message>
</messages>
<customerProfileId>10793616</customerProfileId>
<customerPaymentProfileIdList/>
<customerShippingAddressIdList/>
<validationDirectResponseList/>
</createCustomerProfileResponse>