Hello, Blaine,
X-Cart 4.7.5 doesn't support PHP7.1 by default.
The best way to solve it is to upgrade to X-Cart 4.7.9 which even supports PHP7.2
https://www.x-cart.com/blog/x-cart-v4-7-9-released-skrill-paypal-updates-store-notifications-seo-bug-fixes.html
Alternatively, you can apply the attached patches to make X-Cart 4.7.5 PHP7.1 compatible.
PHP7.0Critical.4.7.5.diff
PHP7.1Critical.4.7.5.diff
As for 3rd-party skins/modules I suggest you refer to the mod's authors.
The quickest way to localize the problem with the white screen is checking for var/log/x-errors_php-<date>.php log files.
Do you have such a file?
var/log/x-errors_php-<date>.php
Thank you.