Let's ask a dumb question: what would make it Prime to those who think otherwise? I mean, by my count, we are well past 200 pages and the only thing gained is increased blood pressure in some and a lot of meme posting.
If you get increased blood pressure from an online forum, you're doing it wrong.
And memes are great! We need more.
As to you question what can make STD Prime...
*Detmer* I am detecting a 25% amplitude mega technobabble demodulation wave coming from Sol
*Saru* Evasive action! Raise shields. Contact Pike on the Enterprise. Tell them to raise shields
*Detmer* Shields not responding! Enterprise is not raising shields either.
*Saru* Brace for impact!
*Detmer* Impact in 3...2...1..
*Saru* Status!
*Detmer* Umm, something happened. My uniform... It's different.
*Saru* Look at the screen. The Enterprise... it's changed. It's different somehow...
*Stamets (from engineering)* WTF did you do to the spore drive? It's gone!
*Rhys* I have accessed our database. Klingon ships, sir, They are all different! Klingons, they are all different!. What is going on?
*Saru* I don't know. Contact Starfleet over holocomm.... Wait, where is the holocomm?
*Rhys* Starfleet records also show no major encounter with the Klingons in the last 12 months! Sir, according to this, we were never at war with them!
*Saru* Michael, where are we? Scan for quantum change.... Michael? Michael? Where are you?
*Owosekun* I have checked Starfleet records. There is no record of Michael Burnham every existing. It shows Commander Spock is the only child.
*Tilly* Holly fuck! I like this new timeline.
Problem fixed. The whole scene could take 5 min or so total. Voila, STD is now in Prime universe.