Why don’t you read some of Diane Sykes written opinions?
https://openjurist.org/453/f3d/853/christian-legal-society-v-e-walker-c-j
Her philosophy is absolutely consistent with Justice Scalia’s.
I’m sorry. I want to be able to support a female judge because she will have an easier time in confirmation. But the two cases you cite and not representative of anything impressive. Chicago had an extreme gun ban and she granted a preliminary injunction. The ban was ridiculous. The case was a lay down for the plaintiff. And, the other case was a university policy against a private club having a Christian adherence pledge. Again, any attorney who lost that one should have to go back to law school.