The prognosis for using Tapatalk with XenForo seems poor.
If anyone is interested in the related threads at the key players websites:
@
XenForo -
Tapatalk work on XenForo 2.1
@
Tapatalk -
Xenforo 2.1 Tapatalk compatibility
ETA: I should've mentioned that there is a plugin with which the new website can update its Tapatalk capability (if it has Tapatalk); but, that website doesn't mention including it in its plans. They just don't seem to be interested saying:
The site is optimized for all screen sizes, including mobile. All features are available and ready to use on all devices.
You might need to start a petition on behalf of those who like to use Tapatalk across multiple websites.