They tried a couple of times (not been keeping tabs on them too closely) to get a root cert into Mozilla - https://bugzilla.mozilla.org/show_bug.cgi?id=1232689 but were denied until they get a valid BR audit, https://bugzilla.mozilla.org/show_bug.cgi?id=1331364 But has yet to answer the follow up questions so the request hasn't progressed.

They published a response to the backlash - http://mic.gov.kz/en/news/matters-using-registration-certifi... saying that it would only be used to improve the security when accessing foreign resources, battle porn terrorism and transnational crime.

Dunno what the adoption rate of the cert was or if they do force the use of the cert when accessing foreign https sites

They quietly removed the notice off the telecom's websites saying that people will need to install the cert or may lose access to foreign https sites (not from kazakhstan) but I would expect someone would of gotten word out if they had (Maybe they did and i've just not come across it).