Hey!
Generally I don't care what time of the month it is, but I know of a few reasons for why people would want to take that time off:
First, yoga philosophy states that going upside down during that time can screw things up, and this has become semi-cultural in the West, in that a lot of people who don't know where this rumour started, or aren't into yoga, still hold to this belief. However, as far as I'm aware, medical science hasn't found anything wrong with being upside down (it's totally up to the person, though!)
Secondly, you are a lot more sensitive to pain when you are close to that time of the month. Honestly, if you're booking piercings, tattoos, or anything else you believe will be painful, I would say aim for mid-cycle. For pole, some people just find themselves more sensitive and can deal with it, and others find themselves really hurting. It all depends on you!
Lastly, is the other physical factors. I know that my cycle is really tough on the system- I get lethargic, and my core works so hard on that task that it doesn't want to do anything else. I get hot easily and for a long time, I'm whiny and undermotivated, and... I just don't want to do things. Rock climbing is hard, poling is hard, getting off the couch is hard. Sometimes, I have cramps so bad I can't move (not when I'm on the pill, though, thank goodness!), and sometimes... none of this stuff happens and it's awesome!
:)