But merely saying "I'm taking next Wednesday off to celebrate Eid" ought to be fine everywhere, as is "this weekend I'm singing in my church choir then going for a picnic".
Similarly, wearing a wedding ring or mentioning that you have a partner should never be a problem, but issuing a company-wide invite to your next sex party likely will be.
"Personal" isn't a synonym for "intimate". It's reasonable to assume that people are able to share the former without forcing their colleagues to deal unnecessarily with the latter.