It's not incompatible with any boot2. Boot2 is part of the console's initialization. It may not have a vulnerable boot1, which is what is needed to install BootMii natively.
The Wii's initialization goes from power-on to reading boot0 from the Starlet processor in the GPU to reading boot1 from the beginning of the NAND to reading boot2 from the NAND. Old Wiis had a flaw in the security signature checks for the console so it was possible to replace boot2 with other code that was signed with an empty key. This signature checking flaw was in the microcode for the GPU so it's not possible for Nintendo to patch it. That's one of the reasons there was a drought in availability about 8-12 months after the Wii was released. It needed a hardware change.
The HackMii Installer will tell you if your Wii has a bad boot1 and if it's the patched one it tells you it can't install BootMii as boot2 so you can only install it as an IOS.
The latest HBC is 1.1.2.
Honestly, I would recommend you ignore everyone else's advice about partial upgrades or using other methods to upgrade. Just update to 4.3 then use Letterbomb to reinstall the HBC and install the latest needed cIOSes. The biggest danger to an official update is if you have modified the actual system menu using themes or patchers. In that case just post what they are and we can help you remove them to get everything square again.
Note there is always a chance of bricking the console with any update whether official or using ModMii or DOP-Mii. If you're concerned about that and can get any homebrew to run then try running
SysCheck and post the .csv file in spoiler tags and we can look at it and try to help. Please use the version in the link as older ones aren't as reliable.