I have an MFA in merchandising and I get asked the question of how it relates to my current career semi-frequently. For many people, there's a disconnect between merchandising and UX, but not for me. Merchandising is product development and distribution, generally of a tangible product rather than software (however that tangible product has to be sold somehow, so it likely has at least a website or sometimes an app to go with it).
In my case, I focused my grad school thesis on jewelry design for social change and it included physical products and e-commerce. That meant I had to do a ton of market, competitive, and user research. I had to understand the market, define and understand the user, find the need gaps, figure out what would make people want the product, design the product, oversee the creation of the product, launch the product, determine how to sell the product in an e-commerce/mobile environment, and manage its lifecycle. And all of this was tied to seasonal collections (or "releases"). Sound familiar? If you're in UX or product management, it should.
In addition to general business skills, I also picked up a good amount of product management skills through my graduate degree. And because it was an Master's of Fine Arts (MFA), I refined my design skills, including sketching and drawing, physical product design and QA practices, UI design and usability testing, color theory, presentations and reports, and branding and identity - all of which are incredibly helpful when it comes to UX. And let's not forget technical documentation in fashion and accessory design - "tech packs" in the fashion world are not unlike notated wire frames in the UX world. Both are technical sketches/mockups of the final product with exact specifications for completion by the next person in the process.
I also did more in-depth research than I've ever done in my life while in grad school, up until that point, at least - recent career adventures changed that. And because I was focusing on a real-life business concept, it was as realistic as it could get within the grad school bubble.
This was an ideal graduate degree for me along the course of my product and UX career path, combining business, design, and technology, all supported by research, which is what UX is all about.
It's also worth noting that I completed this MFA while working full-time, so I didn't lose any steam with my career because of school (and I graduated with honors and a 3.9 GPA). The effect was reciprocal - I applied my daily work to my graduate work and my graduate work to my daily work.
So when asked how an MFA in merchandising relates to my career in product/UX and if I'm looking to change careers, my answer is: "It relates in nearly every aspect and nope, I'm in exactly the career I should be in and the MFA helped me get better at it."