This is difficult question to answer in any religion. Buddhism is 2500 years old and has spread from India to Japan. At times it took on a nationalistic tinge and monks of one nation (and implicitly a different order) might receive a hostile greeting in a new land.

Your specific scenario, of a Chan Chinese monk circa. 1300 going to Tibet to greet Vajrayana monks, I don't think there's going to be any problem. China and Tibet were both under the full control of the Mongol Khaans. This period of history is called Pax Mongolica and is famous for being one that is generally peaceful and mildly economically prosperous. In Tibetan it's still normal to use the expression "an old woman with gold on her head" to describe a time of peace, originally used to describe this kind of rule.

In other time periods, the eighth and ninth, when Chinese and Indian schools of Buddhism fought for control over the Tibetan Empire, in the late sixteenth century when the Dzungars, loyal Gelukpas, introduced religious extremism into Tibet and sacked, burned, and destroyed Nyingma monasteries, and even later in the nineteenth century there was a wave of anti-Nyingma extremism in eastern Tibet.