1. Most of the things that are claimed to be "Pagan" (Christmas, Easter, etc.) are not "Pagan". That is reason enough to say it is problematic.
2. The reason they are claimed to be "Pagan" is not rational critical enquiry, but bigotry. The point is to reduce the legitimacy of the tradition, by claiming it is was originally "stolen" or "plagiarised" by dishonest and mendacious figures in the past. Most of the tropes so beloved of modern anti-theists actually originated in Protestant anti-Catholic polemic. So this time of year "Rationalists" all over the world uncritically repeat sectarian polemic as established historical fact
3. Why should we describe anything not uniquely Abrahamic as "Pagan" anyway? Doing so makes little sense from a secular perspective and just creates false connections between diverse and disparate behaviours, cultures, practices and belief systems all over the world. Why should anything not done for Abrahamic reasons be considered to have been done for "Pagan" reasons?
Christianity certainly integrated many aspects of culture, philosophy, etc from its environment, but the major celebrations that people tend to claim are "Pagan" are nothing of the sort.