Why should they not support XT? Have you looked at their privacy policy? --->
https://bitpay.com/about/privacy The built-in extras that come with XT apart from the bigger block size, is no deterrent for them not to accept it... they already infringe on most of those privacy features.
The added benefit is the extra fee's associated with XT and it's bigger block sizes.... something that Bitcoin Core might not feature in side chains as part of Blockstream.
There is always a economic incentive for decisions like this, that makes no sense at all.