mw13, looked up the Michtov meEliyohu. When R’ Dessler calls this shituf and kfira I’m fairly sure this is a borrowed loshon and lav davka, as I said before. This is common in the more recent mussar seforim, he doesn’t mean a psak halocho that he is doing proper shituf which is avoda zoro, see below.
Avi K, see Chinuch 417 who uses the actual word shituf:
תיז. מצות אחדות השם.
שנצטוינו להאמין כי השם יתברך הוא הפועל כל המציאות, אדון הכל, אחד בלי שום שתוף, שנאמר שמע ישראל ד אלקינו ד אחד
The christians are just one example of shituf, and that is the main reason people talk about shituf as its relevant nowadays, but it isn’t the definition of shituf. The definition is believing there are other gods apart from Hashem (as opposed to saying there is only a different god and not Hashem). Whether you believe that god is somehow part of Hashem, or works together with Hashem, or is Hashems enemy or something, that is called shituf, because you don’t believe ד אחד.
Ramban on the possuk of shema brings from Chazal:
רבי נתן אומר מכאן תשובה למינים שהם אומרים שתי רשויות הן שכשעמד הקב”ה על הר סיני ואמר אנכי ד’ אלהיך מי מיחה כנגדו
Hence this is coming to forbid us to believe there could be another god who would want to make a macho’oh against Hashem and say I’m also a god. Both Avi K’s and mw13’s explanations of shituf would make this medrash hard to understand.
But I haven’t learnt meseches avodo zoroh yet so I may well be wrong.