I believe during a government shutdown ONLY the members of congress who could come together and find a solution by compromising like adults should have their pay stopped. All other government workers, i.e. the military, the police, firefighters, postal workers should still get their pay. It is not their fault that there is a government shutdown that is a failure of Congress…
Congress typically approves back pay so government employees may suffer from a delay but not loss of pay. In fact, furloughed employees get time off with pay. Not a lot of uproar about that. See this:
Federal government shutdowns have historically impacted employees’ pay, with back pay provisions varying across different shutdowns. Below is an overview of the last five significant federal government shutdowns, focusing on back pay arrangements for federal employees:
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2018–2019 Shutdown (December 22, 2018 – January 25, 2019):
• Duration: 35 days
• Back Pay: The Government Employee Fair Treatment Act of 2019 was enacted during this shutdown, ensuring that federal employees received back pay for the duration of the shutdown.  -
January 2018 Shutdown (January 20–22, 2018):
• Duration: 3 days
• Back Pay: Congress passed a continuing resolution that included provisions for back pay to federal employees affected by the shutdown.  -
October 2013 Shutdown (October 1–16, 2013):
• Duration: 16 days
• Back Pay: Legislation was enacted to provide back pay to furloughed federal employees after the shutdown concluded.  -
December 1995–January 1996 Shutdown (December 16, 1995 – January 6, 1996):
• Duration: 21 days
• Back Pay: Congress approved back pay for federal employees furloughed during this period.  -
November 1995 Shutdown (November 14–19, 1995):
• Duration: 5 days
• Back Pay: Similar to the subsequent shutdown, back pay was authorized for federal employees affected by the furlough. 
In each of these instances, Congress took action to ensure that federal employees received compensation for the period they were furloughed due to the shutdowns. The enactment of the Government Employee Fair Treatment Act of 2019 has since provided a more standardized approach to back pay for future shutdowns.