Yay a topic I know all about! First of all this 100% has to do with the fight between WDC & WDSF.
In short, what is happening in Canada now is what currently exists in the US. Two associations who will represent amateurs. One association under WDSF and one under WDC. So, Dancesport Canada (& its American counterpart, USA Dance) are under WDSF, and NDCC, which is the new amateur branch of the CDF (& its American counterpart, NDCA) are under WDC. Fortunately for amateur competitors, you can pay to get memberships to compete in both ($$$), and you won't be penalized if you do so. Additionally, for amateurs, NDCC rules only go into effect on january 1st, so you are free to compete at any competition (minus the ones sanctioned by Dancesport Canada)
As for competing in the US, you will technically only be allowed to compete with the matching association in the US (unless you pay for both memberships, or compete at collegiate competitions). However, in my experience, NDCA doesn't care if you have a number, although that might change now that NDCC exists.
I don't compete pro/am, but this will affect pro/am, mostly because pros CAN be penalized for competing across associations, so I assume they would have to choose a side and stick with it. On the amateur side, I can tell you that in Montreal, at least with those I have spoken to, most people (including myself) are not registering with Dancesport Canada/Dancesport Quebec this year, mostly because it's just not worth it.
For more information, I found this to be rather informative and explains CDF's reasoning behind the creation of the NDCC.
[I can't post links] dancecouncil ca /2014/08/ important-message-board-cdf/
Hopefully that answered your question!