It would easy to tell you to keep your eyes open and do not try to offend anyone by race, gender, religion, sexual orientation, etc. I could give you many examples of not to offend (i.e. Miley Cyrus). However, these next several weeks, companies really need to have their eyes, ears, blinkers and blind spots wide open.
This is the start of a series of religious events. Yes, religion should be not part of work, but you can’t take the religion (or spirit) out of the employee. If you notice an employee is standoff-ish or not doing their normal routine, do take note. However, understand the background of the person, if you have or have not met the person. Look at any accessories and clothing of the person, talk to your employee, and/or do a profile search on the Internet of their background. I would also encourage HR to look at the various religions to understand most of these backgrounds.
There will be moments that religion and policies may intersect. I recommend to HR to be open-minded during these several weeks, because don’t let your company be liable for discrimination, even for the smallest of acts. Be transparent and talk to your employees about why they are doing this and do not assume anything. You get an understanding where they are coming from and HR will layoff the accelerator a bit, depending on their reason. Now, if they are continuing to do what they do after the season is up, then investigate the matter and make a final decision on what to do with the employee.
So for these several weeks, pay attention to the company’s policies and procedures, but also pay attention to your employee. Do not penalize your employees, talk and collaborate with them. It is the only way to get a definitive answer.