As a woman, her stance on abortion would be a major issue, and as SD Governor she supports that states very strict anti-abortion laws (life of mother only). That is more hardcore than Trump’s own position seems to be and much harder than where he’s said the R party needs to be to win.
Noboby’s going to look at any VP candidate as a factor with regard to foreign affairs or even trade (because that’s Trumps long suit) but they’re damn sure going to look at a female VP as a rorsharch test for abortion and Noem is not a plus in that regard.
None of the pro-abortion females will be voting the Repub ticket anyway. So it shouldn’t matter how strict her position is on that subject as far as alienating any Trump voters is concerned.