Hope you have a quick and smooth recovery from your surgery.
Those aren't mutually exclusive concepts. They do care about what is going on with the other Clans, and they are also very focused on what the other Kindraa are up to.
Often the events in the Homeworlds do affect them. Some Kindraa also intentionally target the other Clans, particularly for genetic material (looking at Sainze and Payne). In the margins of their section of FM: CC you can see their prevailing attitude toward each of the other Clans, and they do have one, and its mostly a negative view for many of them. They even go so far as to suggest in the Clan Wolf one that Clan Wolf could have avoided the schism between Clan Wolf and WiE had they settled their Crusader/Warden differences as the Mandrills would have, via internal Trials. So they have some contempt for most other Clans and even some almost Falcon-like arrogance that the Mandrill ways are best.
The Sharks and eventually the Blood Spirits aside, it just seems like most activity with the other Clans takes the form of Trials against those other Clans (as opposed to more diplomatic negotiations/politics). There are Trials against the other Clans, such as Trials of Possession, there are hints of that scattered throughout Mandrill history. So yes, they care. Yes, they are keeping informed about what's happening beyond their Clan. After the Smoke Jaguars were gone, the Mattila-Carrols scrambled to contest Pahn City on Huntress. The Vipers and Mandrills were fighting on Marshall and the Coyotes and Mandrills were fighting on Atreus (FM: WC). That's just a few examples, there are plenty more referenced in various books. Trials for territory, resources and genetic material.
But also, yes, that Kindraa rivalry stuff (which rises to the level of a feud or vendetta quite often and is likely felt on a very personal level for many Mandrills) is very much at the forefront a lot of the time. It probably dominates the day-to-day for most Mandrill warriors for much of the Clan's history. The Mandrill preference is to settle every difference within the Clan via combat. Even Khan elections are handled via Trial of Possession. With all of this internal fighting going on at the intensity of a feud/vendetta, it makes sense that there have been long stretches of time when the average low-to-mid ranked Mandrill warrior felt like whatever was going on with the other Clans was mostly background noise to the Kindraa feud/vendetta that was fueling them most days.