Basically, the decision at play here, that your superiors would have to make when deciding to promote you into a position where you might interact in person with customers or business partners, is "do I want this guy meeting the money people face to face?". That is a question that requires a look at various aspects of you from both a personal and professional standpoint, including your speaking skills (including impromptu), your wardrobe choices, and personal hygiene and grooming. There are plenty of very highly-skilled, talented members of the workforce who don't give a flip what they look like or even what they smell like. As a senior manager, you generally do not want these people representing your company in person, however high the quality of their work is behind the scenes. This is where this kind of thing becomes a bar to advancement.
Various things come in and out of fashion; facial hair is one of them. Clean-shaven is pretty much always fashionable, while facial hair runs on about a 30-40-year cycle. Facial hair denoted the hippies from the "normies" in the late 60s, then mustaches became fashionable in the 70s, then it was back to clean in the 80s and 90s, and then a close-trimmed beard with various amounts of trimming work started coming back into fashion in the 2000s. The driver of this current trend is a change in the perception of wealth over the last couple decades; "new money", the dot-com startup types and young celebrities, cultivate a look that says "I'm wealthy enough, smart enough and busy enough to not have to care whether I shave every day". Therefore, while fashionable, it still gives the impression that maybe you don't care how you look. That's typically not a good image for a business type to be projecting.
So, in summary, the expectation in most of the business world is to look clean and presentable. Beards are generally acceptable as long as they look well-groomed, but getting and keeping it acceptably clean-looking could be more trouble than it's worth versus just running a razor over your chin every day.