Maggie's Farm

This disingenuous argument has been making the rounds in the left-wing echochamber, so it is worth addressing.

Trump's Executive Order (EO 14399)
Requires states to provide voter-eligibility lists;
No. "the Secretary of Homeland Security, through the Director of United States Citizenship and Immigration Services and in coordination with the Commissioner of SSA, shall take appropriate action to compile and transmit to the chief election official of each State a list of individuals confirmed to be United States citizens who will be above the age of 18 at the time of an upcoming Federal election and who maintain a residence in the subject State (State Citizenship List). The State Citizenship List shall be derived from Federal citizenship and naturalization records, SSA records, SAVE data, and other relevant Federal databases." Emphasis mine.

Authorizes the USPS to refuse to deliver mail ballots if states do not comply with the new requirements;
No. Nowhere does this say that.

Directs the creation of a 'citizenship list', which will almost certainly be inaccurate and incomplete;
Well which is it? Are the states to provide this or does this EO direct it? If the latter, if you don't think the Federal Government can handle this without accuracy and completeness, how do you expect them to accomplish anything on a national scale, like, I don't know, health care? No fly lists? Taxes?

Calls for the investigation and prosecution of state and local officials who issue ballots to ineligible voters. While the statute requires intent, the executive order notably leaves that out.
Sec. 5. Enforcement. The Attorney General and the heads of executive departments and agencies (agencies) with relevant authority shall take all lawful steps to deter and address noncompliance with Federal law, including withholding Federal funds from noncompliant States and localities where such withholding is authorized by law. Evidence of violations of existing Federal laws by State or local election officials; States or localities, including any instrumentalities thereof; contractors; individuals involved in the administration of Federal elections; or public or private entities engaged in the printing, production, shipment, or distribution of ballots may be referred to the Department of Justice for consideration of investigation or charges under 18 U.S.C. 2(a), 18 U.S.C. 241, 18 U.S.C. 371, 18 U.S.C. 611(a), 18 U.S.C. 1001, 18 U.S.C. 1015, 52 U.S.C. 10307, and 52 U.S.C. 20511. States and localities should preserve, for a 5-year period, all records and materials — excluding ballots cast — evidencing voter participation in any Federal election (e.g., ballot envelopes, regardless of carrier).
Looking, looking, looking, nope. Can't find where it requires "prosecution of state and local officials who issue ballots to ineligible voters." Investigation, yes. Consideration of charges, yes. Prosecution requirement? Nope.