All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
The Fatwa to which you referred does not prohibit referring to them as Christians. Rather, it underlined that it is better to use the term used in the Quran and Sunnah, namely the Nasaara (Nazarenes), and it also highlighted the fact that some Muslim scholars referred to them as Christians. So, it is not prohibited let alone a grounds for declaring someone an unbeliever.
Indeed, declaring someone an unbeliever is a serious matter that should not be dealt with hastily even if someone actually committed an act of unbelief. This is because there are certain conditions that must be fulfilled and impediments that must be absent before declaring a Muslim an unbeliever. For more benefit, please refer to Fataawa 721 and 14489.
Referring to the Nasaara as Christians does not necessarily mean that one considers them to be believers. It is a mere description of the current situation, namely their claim to be followers of Christ something which is not problematic.
Moreover, the Nasaara did not follow the religion which the Maseeh (Messiah) presented but rather opposed it and distorted their divine scripture. This however is not a reason for prohibiting referring to them as Nasaara.
Allaah Knows best.