It is hard to figure out what R. Shimon ben Yochai is saying in Sanhedrin 63.
There is one question because the verse he brings does not distinguish between "joining" (שיתוף) and regular idolatry בלתי להשם לבדו [To God alone].

So let me lay out the basic paragraph and then I will say over the problems.

 Rabbi Meir said, "If not for the letter "vav" in 'these are your gods, O Israel, which brought you out from Egypt,' the Jewish people would have been destroyed."

R Shimon said, "Anyone who joins the name of Heaven with something else is uprooted from this world. Rather it means they desired many gods."

What it seems at first glance  is this. It would not have mattered if they had done pure idolatry or joining--in any case they would have been destroyed. Rather they only desired other gods. This makes sense. But then what do we do with the fact they said, "These are your gods Israel." They did more than desire. They accepted.

So now we understand why Rashi said in fact just that: They accepted other gods. But then what is R. Shimon saying?

Now just to be clear, the verse בלתי להשם לבדו "To God alone" is from the verse "He who sacrifices to the gods will be destroyed,.. only to God alone." Exodus 32. That is: One must not sacrifice to the gods, only to God. This does not distinguish between to other gods and to other gods with God. As far as this verse is concerned it is all the same thing. One must sacrifice to God alone, and anything else is bad.

And I hoped to get insight by opening up the Talmud in Suka 45b. But so far I have gotten nowhere.

What I had thought at first is R. Shimon is saying joining something with God is worse than straight idolatry. And if that was the case, everything would be OK except the verse "To God alone." --which has one complete set of services towards God alone--and everything outside that set is not OK.

This is relevant modern day issues because Christianity is considered by Tosphot to be "joining" [Sanhedrin 63b].  That is Tosphot thinks Christianity is joining someone to God. But then he says gentiles are not commanded against this. But why not?
In any case, it looks to me that Tosphot is right because even Thomas Aquinas has trouble getting past the idea that the physical body of Jesus was God. I forget his answer but at the time I read it, it did not sound very convincing. I will leave that to  modern Scholastic Scholars like Feser.