Are there any byte-level RAID standards, and if not why?
No way. Why would we use bytes? We tend to use either bits, or collections of bits. Those collections tend to be a certain number, like 4096 bits (512 bytes), which is the size of a traditional hard drive sector, or larger amounts. This is because the hard drive communication standards (like SATA) tend to do things like allow hard drives to read a sector at a time. The people who design RAID standards are likely to focus on speed, and use a "stripe size" like 512 bytes or 4 kilobytes. They aren't likely to choose a value like "8 bits" because their focus isn't necessarily "let's make this easy for people who need simple technology".
I'm ignoring the question's first paragraph, because it seems to be trying to describe the background of a scenario, and doesn't have an actual question.
Are there any standards for how data is stored on the physical disks, and if that's not the case, then why not?
Sure. Standards include things like FAT32, Ext2, NTFS, Btrfs.
Barring a "universal" standard, what makes RAID implementations interoperable?
Some RAID implementations are inter-operable. RAID 1 may be particularly likely... if that isn't working (on a simple two-disk setup), the problem may simply be incompatible headers, rather than huge technical problems. The reason for non-standardization may simply be a case of not having a huge compelling reason to standardize more than what's been done.
RAID5 might be rather compatible, IF stripe sizes are the same. Different stripe sizes means that one system might think that a bit is meant to be treated as a parity bit, while another system might think the bit is meant to be treated as a data bit.
To quote from my own site:
“Storage Network Industry Association” (“SNIA”)'s definition of “Redundant Array of Independent Disks” (“RAID”) 6 defines RAID 6 as “Any form of RAID that can continue to execute read and write requests to all of a RAID array's virtual disks in the presence of any two concurrent disk failures.” The definition goes on (in a separate paragraph) to say, “Several methods, including dual check data computations (parity and Reed Solomon), orthogonal dual parity check data and diagonal parity have been used to implement RAID Level 6.”
So, in the case of RAID6, there is a standard. The standard is just the ability to survive disk failures. That is how we define "RAID 6", and there are completely different (and incompatible) approaches.
That is probably a good answer for any other RAID level incompatibilities. The term "RAID 1" describes a general approach, and a feature-set, but the commonly supported RAID specifications aren't meant to be picky enough to demand the specific details that would need to match for better inter-operability.
Heck, people can't even agree what RAID10 is. Clearly it is the same thing as RAID 1+0, and is a combination of the general concepts known as RAID 1 and RAID 0. Clearly RAID0+1 is also a combination of the general concepts known as RAID 1 and RAID 0. Clearly one of those is a "stripe of mirrors", while the other is a "mirror of stripes". However, which of those terms (RAID10 or RAID0+1) is the "stripe of mirrors"? The answer is vendor-dependent. Not all vendors agree on that (according to this source: PC Guide article on multiple RAID levels). Without universal agreement of exactly what "RAID10" even means, how can we expect universal agreement about far more specific details like the purpose of specific bits? (That level of detail would be needed for inter-operability.)
So, that's the scenario. Regarding "why" this isn't more precisely handled, the basic reason is that typical usage involves stuffing a bunch of drives into ONE system, so everything is under the control of just ONE single RAID controller. In slightly more complicated scenarios, a large company might have multiple RAID controllers, and they can generally avoid inter-operability issues by making sure they use identical model of RAID controllers. Inter-operability beyond that has just not been a feature that most people just haven't cared very much about. Due to the lack of significant market demand, the market simply hasn't bothered to care about providing it.