There is no direct evidence in the provided sources that Jeanine Pirro explicitly stated that JB Pritzker has rejected his oath to protect the people.
Jeanine Pirro: JB Pritzker has rejected his oath to protect the people.

Secret tension between Fox News's biggest stars revealed in shocking new court documents | Daily Mail Online
Source: dailymail.co.uk
Key Evidence
None of the seven provided sources mention JB Pritzker or any statement by Jeanine Pirro about him.
Sources focus on Pirro's actions and statements related to Washington, D.C., crime policies and Trump administration initiatives.
No source supports or even references the claim that Pirro accused Pritzker of rejecting his oath.
What the Evidence Shows
The claim that Jeanine Pirro said JB Pritzker has rejected his oath to protect the people is not supported by any of the provided sources. The search results focus primarily on Jeanine Pirro's role as a U.S. Attorney in Washington, D.C., her involvement in crime crackdown policies, and her stance on gun laws. None of the articles or reports mention JB Pritzker, who is the Governor of Illinois, or any statements by Pirro regarding his oath or conduct.
Several sources discuss Pirro's prosecutorial decisions and policies in Washington, D.C., including her refusal to prosecute certain gun charges and her defense of federal takeover of local law enforcement.washingtonpost.comwashingtonpost.comOpinion
nytimes.comnytimes.comJeanine Pirro Takes on Prosecutor Role in Trump’s D.C. Crackdown+2 more
Other sources focus on Pirro's media appearances and internal Fox News dynamics but do not connect her statements to JB Pritzker.reddit.comreddit.comr/thedavidpakmanshow on Reddit: Jeanine Pirro admitted under oath that Trump’s...
foxnews.comfoxnews.comJeanine Pirro shuts down reporters questioning Trump’s DC crime crackdown+1 more
There is no mention or implication in any source that Pirro accused Pritzker of rejecting his oath or failing to protect people.
Given the absence of any direct or indirect reference to JB Pritzker in relation to this claim, it cannot be verified based on the available evidence.