This is the most misunderstood date in the Christian calendar, and the explanation contains no theological disagreement at all.
Every church that keeps the nativity keeps it on 25 December. The difference is which calendar the 25th is counted on. The Julian calendar, in use in the Roman world from 46 BCE, assumes a year of 365.25 days, which is about eleven minutes too long. Over centuries the error accumulated, and by 1582 the calendar had drifted ten days out of step with the seasons. Gregory XIII corrected it by dropping ten days and by changing the leap year rule so that centurial years are leap years only when divisible by 400.
Catholic states adopted the reform at once, Protestant states over the following two centuries, and Britain in 1752. Orthodox churches did not, and the offset has since grown to thirteen days. So 25 December in the Julian reckoning falls on 7 January in the Gregorian one, and will do until 2100, when the gap becomes fourteen days and the correspondence shifts to 8 January.
Not all Orthodox churches are on the old calendar. In 1923 a congress at Constantinople adopted a revised Julian calendar for fixed feasts, and the churches of Constantinople, Greece, Romania, Bulgaria and others follow it, so they keep the nativity with the West. Russia, Serbia, Georgia, Jerusalem and the monasteries of Athos retain the old calendar. The Armenian church is a separate case again, keeping the nativity on 6 January with the Epiphany, which reflects the older undivided feast.
Nobody is celebrating a different event, and nobody is thirteen days late.