Its not just Muslims who struggle with having a unifified date for events
Christians hope to unify the date for easter within the next 5-10 years. The western churches have it often a week earlier than the orthodox church.
(Christmas is a less remembered one, where AFAIK the orthodox church ceebrate it on 6 January).
However, having different dates should not be an issue for disunity - there are accounts from the times of the sahabah of differing locations starting ramadan/eid on different days and this was allowed and not condemned.