For those who misunderstand and misapply the gospel message, you betcha.
I have no fear, worry or anxiety in regards to my standing with God.
You may consider this arrogant. I consider it nothing of the sort, because I am not relying on my performance in regards to that standing. To rely on my performance and consider myself worthy would, indeed, be arrogant.
My standing is secure because I rely on the finished work of Christ.
But, to your point. Yes. Many misunderstand the gospel and live in constant worry and fear. This worry and fear usually translates itself into pointing out flaws and missteps in others, hoping God will either (1) find the one person "better" than the other or (2) focus His attention elsewhere.