As a non-Christian, I never made that Xmas connection.
Well, as a Christian, I wouldn’t feel bad about it because the poster is not correct. The X in Xmas does not stand for a cross, it comes from the Greek spelling of Christ which is Χριστός. The chi-rho symbol (☧) is an imposition of the first two letters (Χ and ρ) and is still commonly used to refer to Christ in some denominations.
As a bonus: if you’ve ever wondered (or not wondered) why some Christian symbolism uses a fish, ἸΧΘΥΣ (or ICTHYS) is an acronym for Ἰησοῦς Χρῑστός Θεοῦ Υἱός Σωτήρ, “which translates into English as ‘Jesus Christ, God’s Son, Savior’.” (en.wikipedia.org/wiki/Ichthys) This has been used since the first century.