the term Initiative is well defined as being all three factors of Initiative Attribute, Initiative Score, and Initiative Dice. That part is not really something that can be debated, is it...? (well, everything can be debated i guess - but at least that part is very straight forward and very hard to read in any other way).
that single line of text make it rather hard to argue that for example an enhancement to initiative score would be compatible with an enhancement that is incompatible with enhancements to initiative.
it also make it very hard to argue that an enhancement to intuition which is part of the initiative attribute would be compatible with an enhancement that is incompatible with enhancements to initiative (for the sole purpose of calculating the initiative attribute - it is of course still compatible with an enhancement to intuition for the purpose of calculating the pool for a defense test or whatever that does not have anything to do with the initiative attribute, initiative score or the initiative dice).
just because two enhancements are incompatible does not mean you can't acquire them both. incompatible just mean you have to select when and where you want to use one or the other enhancement.
...for example having wired reflexes 1 and improved intuition spell would be incompatible for the purpose of calculating initiative attribute which is part of initiative, but would be compatible when using intuition for calculating the pool for a defense test. being in astral projection would possible give you on average a higher initiative score if you depend on the intuition spell enhancement rather than on the wired reflex enhancement (since the reaction attribute part of wired reflexes is not used to calculate initiative attribute when in astral space and the intuition attribute is counted twice when you calculate initiative attribute when in astral space - which might overshadow the extra initiative dice you would get from wired reflexes).
...while an enhancement to reaction would be incompatible with wired reflexes for all purposes, not just for calculating the initiative attribute (except if the enhancement to reaction is the reaction enhancer cyberware and they are both set to wireless ON).