Same side as who?
It's not an R v D thing. It's not even a US specific thing.
I'm not saying there is merit to the theory, but I think you're misunderstanding the story laid out by these releases. The "sides" are the rich and powerful vs everyone else. She's clearly in the "everyone else", camp, regardless of what boots she's licking.
For iberville and assumption, in the presidential elections, support between R and D has moved within bounds of like, 2%, for the last 3 presidential elections.
In that same time frame, the maximum support a republican candidate for the 60th house of representatives has been 18.8%. Not margin, TOTAL.
Don't get me wrong. It's not bad news. But the reality of this outcome in this district is "No material shift in voting patterns in area over the last 20 years".