Your perception is a bit off. According to each institution's current enrollment websites, in the 2020 class, 45% of Purdue (main campus) students were Indiana residents, while 59% of IU Bloomington students were Indiana residents. Also, when you take each institution's system into account, IU enrolls and graduates far more Indiana residents than any other institution or system in the state, and it's not even close.
Looking at cost, Purdue's in-state pre-aid tuition and fees are $9,992, while IU's are 11,220, a difference of $1,228. While it's a difference, that's not a terribly significant dollar amount. Again, that's all pre-aid. Taking aid into account, Purdue's average in-state cost is $12,527 while IU's is $13,428, a $901 difference (from US News data). IU and Purdue both rank near the bottom of the Big 10 in terms of average net cost to student.
As for admissions, both schools basically admit the same student profile, although Purdue's admitted student profile is just a tick higher (think roughly 1 ACT point).
I think your perception of the institutions is common across the state. IU gets the "elitist" designation even though it serves more Hoosiers, produces more native graduates, does it at a cost that is only marginally higher, and admits basically the same student academic profile as Purdue. I think that's more of a product of each institution's culture and academic strengths (and how they are valued in the state and politically) in addition to the political perceptions of its leaders. It's certainly not an accurate product of any data point or metric.
