Answer
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 `alayhi wa sallam ( may Allaah exalt his mention ) is His slave and Messenger.
There is no doubt that it is most appropriate to use the Hijri calendar because it is the Hijri year that includes the lunar months which Allaah made as measurement of time for the people, for Hajj, fasting, and the sacred months, and it is by these months that the days whose fast is recommended are known. Allaah Says (what means): {They ask you, [O Muhammad sallallaahu ‘'alayhi wa sallam] about the new moons. Say, “They are measurements of time for the people and for hajj [pilgrimage].”} [Quran 2:189] Moreover, Allaah Says (what means): {Indeed, the number of months with Allaah is twelve [lunar] months in the register of Allaah [from] the day He created the heavens and the earth; of these, four are sacred. That is the correct religion.} [Quran 9:36] Also, the Prophet sallallaahu `alayhi wa sallam ( may Allaah exalt his mention ) said: ''The year is twelve months, four of which are sacred, three are consecutive: Thul-Qi’dah, Thul-Hijjah and Muharram, and the fourth one is Rajab of Mudhar, that comes between Jumaadah and Shaa’baan.” [Al-Bukhaari]
Therefore, it is most appropriate to use the Hijri calendar as we clarified but we do not have evidence prohibiting the use of the Gregorian calendar even though one should not restrict himself to the use of the Gregorian calendar only. Indeed, the Hijri year is the calendar exclusive to the Muslims, and they need it for their festivals, their acts of worship and their dealings – like Hajj, fasting, the waiting period [for the divorced or widowed woman], breastfeeding children, Zakaah and so forth.
The Hijri calendar is based purely on the lunar months; Allaah Says (what means): {They ask you, [O Muhammad] about the new moons. Say, “They are measurements of time for the people and for hajj [pilgrimage].”} [Quran 2:189]. Therefore, a Muslim should not abandon the Hijri calendar and the lunar months to use any other calendars.
Allaah Knows best.
So no. While the Hijri calendar is primary, it is not forbidden to use others as well, and thus no stricture against celebrating a world recognized New Year. They just need to ensure they follow the Hijri calendar for its events. As for what is in the glass, my own kids and I drink "sparkling grape juice", which is just juice that has carbonated to look like champagne, but is not.