There is a famous debate between Rashi and Ramban about the order of events between the last few parshiyot. We are given this whole interlude about the details of the Mishkan and Priestly Garments, in between Har Sinai, the Revelation and the Ten Commandments, and the Golden Calf incident.
Why is the Mishkan specifically discussed right before the Golden Calf?
I believe it is the Netivot Shalom or the Or HaChaim, who asks the question why the Mishkan was necessarily so grand, magnificent, laden with gold, etcetera, etcetera. Does Hashem need a golden palace? A bit haughty, no? Well, after Am Yisrael sinned with the Golden Calf, it became evident that their majestic G-dly figure was attributed the aspect of gold. Since Am Yisrael associated gold to G-d, so too, the Mishkan necessitated being made of gold and grandeur.
However if we take it one step further, the poskim teach of an eternal link between the teshuva (repentance) the Mishkan and the Golden Calf. The Mishkan represents Har Sinai, the eternal marriage between Hashem and His People.
Thus, perhaps the para aduma, in my humble opinion - the ultimate return to the natural, the calf without gold, purely red, the color of the earth - is then what provides the ultimate cleansing from sin, into purity, as it is the true final teshuva me’ahava necessary for geula.