The BCRPA seems to be a non profit that is engaged in a number of things: parks and recreation as well as fitness. A regulatory board would seem to me to refer to a governmental agency, rather than a non profit.
Am I correct that the aspect of their group that you are questioning is the registry?
From what I can see (and not being an expert on Canadian regulation, government, or fitness, I could easily be wrong) one can get on the registry by proving a certain level of training and certification. This seems not to be a regulatory thing… that would be more like with massage or nutrition where you have to pass tests and be regulated by the government in order to work. This seems by my cursory view to be more of a way for the industry to provide information in a centralized place for the public…. not that being or not being on it would affect your legal ability to work, but that it is a clearinghouse to compare different trainers and make sure you get someone with a minimum level of training. That is very similar to the Yoga Alliance. Most yoga teachers put themselves on the alliance. The alliance does not train them, but says…. yes, this person has x number of hours of training that meets rigid requirements vis a vis content, and has taught at least x number of hours.
I have no idea whether they do a good job at this, or how many people go on it, but it does not look like it is at all required.
If a high percentage of your colleagues do put themselves on this list, and if it is not too expensive to do, you might find some benefit to be on it. At least it is always good to know what potential employers want. If they don’t care then you probably don’t need to either.