It's a widely-used idiom with no severe connotations, outside of some social media politics bubbles. AFAICT, it's completely normal and tolerated language, *including* within mainstream US-left politics—the other commenters are just wrong about this.

Example usage 1:

- "The ex-chief of staff to former President Barack Obama said Democrats are "the thin blue line" between Americans and the special interests Trump is courting."

https://www.huffpost.com/entry/rahm-emanuel-makes-dark-predi... (Dec 4, 2024)

Example usage 2:

- "Defenders of Democracy: The Thin Blue Line chronicles the causes and consequences of the January 6, 2021 attack on the United States Capitol, Congress, and the electoral certification process featuring perspectives from police officers and family members of fallen officers. The film highlights the gravity of the events that will undoubtedly leave an enduring impact on political history."

https://www.pbs.org/show/defenders-of-democracy-the-thin-blu... ("Defenders of Democracy: The Thin Blue Line" (2024))