Well, I think that mindfulness (whether taught in MBSR or otherwise; MBSR is great, but there are plenty of other perfectly good ways to learn these skills) and acceptance-based approaches are particularly useful when we are dealing with things that are difficult and challenging and also here to stay, much like many aspects of diabetes. Traditional cognitive and behavioral approaches are very change-oriented, and this has its place—we certainly all need to make changes sometimes, including in our diabetes management, and traditional CBT is great at helping people do that. However, a lot of long-term challenges with diabetes or any chronic illness is what do we do with the parts of it we can't change or that continue to be difficult no matter what we do? That's when learning how to accept our reality is essential. Acceptance here doesn't mean "approve" of it; rather, it means to acknowledge the present situation we find ourself in for what it is, rather than focusing on what we think it "should" be. So in general, mindfulness can be a useful tool to help increase our ability to tolerate the stress of managing diabetes and to increase our willingness to engage in the challenges of managing it.
Example: if my blood sugar is 217, I could think about how awful that is and beat myself up thinking about how it should be better and ruminate about how I keep screwing up my diabetes control. That's probably just going to get me frustrated, depressed, and on my way to feeling overwhelmed/burned out though, and, ironically, might lead to less willingness to test next time if I know that if it's a "bad" blood sugar, I'm going to go through all of that. I might end up avoiding testing as a result. Practicing mindfulness in that moment would ideally help me take a few breaths, a step back, recognize that the thoughts I'm having about it all are thoughts going through my head. I'd take a moment and notice my reaction. I'd acknowledge that I'm frustrated and that my blood sugar is higher than I wanted it to be. I wouldn't try to make myself feel any differently, but rather than continuing in my head to beat myself up, I'd try to shift my attention back to the moment at hand. To focus on what I'm going to DO NOW that would be helpful to myself. I might decide to take some insulin and go for walk, and I'd do myself to engage myself in those activities, and if I notice myself starting to get mad at myself for the high blood sugar again, notice that too, but then gently bring my attention back to whatever is around me during my walk, say.
MBSR is one of many interventions that includes mindfulness. It's a good one, and there are many other approaches as well, and it varies tremendously what works for people, just like with any other treatment/approach. You can certainly use the materials on your own; I will say, that often a lot is gained from working through them with an experienced therapist/instructor, especially around the concept of acceptance, which often is very challenging for folks to practice (relative to the present-centered awareness components of mindfulness, which are more straightforward). A book I like on that topic specifically though is Radical Acceptance by Tara Brach (I believe she also has a podcast)—she's great. I also very much like Acceptance and Commitment Therapy (ACT, pronouced like the word "act"), which been shown in RCTs to improve diabetes control. That approach also incorporates mindfulness, as well as identifying personal values and using them to guide action, and often has a more intellectual approach than MBSR (which has more of the meditation class vibe throughout). There's a self-help book for ACT called Get Out of Your Mind and Into Your Life by Steven Hayes that is not specific to diabetes (no more than MBSR is) that I find tends to be particularly appealing to and useful for very logical thinkers (of which there seem to be a number of here)—a lot of it can be easily applied to diabetes/any life struggle.
(Note: I'm not connected to/do not profit from any of these interventions or resources. I've used them in my practice though, although neither my practice nor research involves diabetes—too close to home for my comfort.)