It's more like the plural of 'deer' being 'deer'. I don't think I've ever heard anyone attach an 's' to 'kanji' for pluralization when speaking English. Like how it might be odd to say 'sushis' or 'wasabis'. Whenever I need to stress plurality i would say 'kanji characters' or something like that. Oxford English Dictionary lists 'sushi', 'kanji', 'shinkansen', 'katakana' all as being mass nouns or having the plural form the same as the singular. The exception in the words I looked up was 'tsunami' which may be pluralized as 'tsunami' or 'tsunamis'.
Most of those are the sorts of nouns that wouldn't normally be pluralized in English. "Sushi" is like "rice" — specifies what the roll is made of rather than the roll itself. We don't pluralize the name of a rail system like Shinkansen because there is only one of it (similarly, "the L" but not "the Ls"). But there are many Japanese loanwords that are commonly pluralized differently in English. For example, futons, tycoons, typhoons, tatamis, ninjas and kimonos.
It's ambiguous whether "kanji" is a mass noun referring to the character set as a whole or a singular noun referring to a character in the set. I think it's both. So it seems hard to blame someone for being unclear on the matter.
