I would say Shinto is formed by 神 (shin) and 道 (do). Oh, yes, Japanese kanji has its origin in Chinese hanzi and all of that, as Spanish has its origins in Latin and Greek and... But we do speak Spanish and not Greek. So do the Japanese speak, well... Japanese and not Chinese.
Don't even get started on English being a phonetic language...
I think this needs its own thread.
Chinese and Japanese use similar character systems, it is really the inflection that changes. Technically a Cantonese speaker would say "Shin-Dao". It is inflection in the end.
Regardless, it is splitting hairs.
I agree, English is not entirely phonetic. However that's not what is being argued. Why English speakers spell it "S-h-i-n-t-o" is what is being argued, and those reasons are phonetic in origin.
Again, it is as good as the difference between "color" and "colour".