It is not regarded as befriending them, but it is regarded as imitating them.
The Christian calendar existed at the time of the Sahaabah, but they did not use it, rather they ignored it and used the Hijri calendar.
They established the Hijri calendar and did not use the Christian calendar even though it existed at their time. This indicates that the Muslims should be independent of the kaafirs’ customs and traditions, especially since the Christian calendar is a symbol of their religion, because it is based on veneration and celebration of the birth of the Messiah at the turn of the year. This is an innovation introduced by the Christians, which we do not share or follow, so if we use their calendar that means we are imitating them.
Praise be to Allaah, we have the Hijri calendar which was established for us by the caliph ‘Umar ibn al-Khattaab (may Allaah be pleased with him), in the presence of the Muhaajireen and Ansaar, and this is sufficient for us.