Popularity is always changing, like fashion, it depends on the mood of the community, the offering of certain sets that were highly hyped and such. However, some mounts and profiles have been in the market for longer time and have been included in more keyboards by manufacturers. The first classes are MX and ALPS mounted, that had some share of the market when all the boards were mechanical. In minor volume other mounts were offered like Space Invaders and Topre. MX based caps should be the most popular for MKs by a large amount. As someone already stated, some data should be required to back the statements. Maybe at DT wiki should be some; but, meanwhile someone takes the time to dig into it, this is just a comment based on common knowledge. Buckling spring caps have also its own market and space; but, they should be even less common nowadays than the rest of MK's caps.
In MX mounted caps, OG Cherry and GMK, after it, should be the most common, not necessarily the most popular. Other caps that share the Cherry profile should follow closely, like ePBT and JTK. Regarding other profiles, DSA and its recent relatives should follow closely and then SA and other similar high profiles. I am not certain on the share of DSA against SA, but they should be less than Cherry. OEM profile should have certain share due to the fact that most modern MKs carry them when new and some Chinese manufacturers started selling similar shaped caps some years ago.
My grain of salt.
