Is it permissible to hold celebrations during the Christmas season, knowing that the intention behind the celebration is not related to Christmas, but is rather something completely unrelated except that it is close in time?

There is no harm in celebrating joyful occasions such as marriage or success, provided that it is done only once when the occasion occurs, and not repeatedly, so that it does not become an Eid (festival); because the legislated Eids for Muslims are only Eid al-Fitr, Eid al-Adha, and Jumuah (Friday). As for the annual, repeated celebration of birthdays or wedding anniversaries, it is an innovation (bidah). The permissible celebrations are not harmed by their occurrence during the Christmas season because they are tied to their specific reasons. Sheikh Ibn Uthaymeen issued a fatwa permitting the holding of parties for joy and happiness at the achievement of a desired outcome, not for drawing closer to Allah, warning against extravagance in them.