There are actually many downsides to buying social media followers. For example, if your fans are not actually people interested in your product, this could hurt you if you ever want to run ads on Facebook or have your organic content show. With low engagement, your organic content will not show often on real users' Facebook feeds.
In addition, your targeting on Facebook ads will be hurt by random, uninterested followers. Facebook's computer learning algorithms will look at your followers when serving ads to determine the best people to serve these ads to. If your followers do not represent your actual users, ads will be served to an irrelevant audience.
Lastly, it is fairly obvious when companies are buying fake followers. These followers will often be from random locations and, as previously stated, will not actually engage with your content. Any page with a large number of followers and extremely low user engagement will set of red flags right away and look fishy to your potential customers.
All in all, it much better to have a smaller group of engaged social media followers than a large number of inactive social media followers. If you'd like to get actually engaged users one great tactic could be to build a contest to win one of your products. By using a product such as Rafflecopter, you can allow users to enter your contest by following you on different social media sites.
You can promote a contest through ads on Facebook and Twitter targeted to CrossFit fans and most likely build a pretty solid group of followers that will actually engage. I would recommend against targeting users who are likely to generally enter contests and focus on promoting the contest to users who may actually want to buy your products.