Looks like the crime of publishing a person's tax return isn't that hefty - $5,000 and/or up to 5 years in prison. I opt for the prison term for employees at the NYTimes.
https://www.law.cornell.edu/uscode/text/26/7213
26 U.S. Code § 7213 - Unauthorized disclosure of information
US Code
Notes
IRS Rulings
Authorities (CFR)
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(a) Returns and return information
(1) Federal employees and other persons
It shall be unlawful for any officer or employee of the United States or any person described in section 6103(n) (or an officer or employee of any such person), or any former officer or employee, willfully to disclose to any person, except as authorized in this title, any return or return information (as defined in section 6103(b)). Any violation of this paragraph shall be a felony punishable upon conviction by a fine in any amount not exceeding $5,000, or imprisonment of not more than 5 years, or both, together with the costs of prosecution, and if such offense is committed by any officer or employee of the United States, he shall, in addition to any other punishment, be dismissed from office or discharged from employment upon conviction for such offense.
(2) State and other employees
It shall be unlawful for any person (not described in paragraph (1)) willfully to disclose to any person, except as authorized in this title, any return or return information (as defined in section 6103(b)) acquired by him or another person under subsection (d), (i)(1)(C), (3)(B)(i), or (7)(A)(ii), (k)(10), (l)(6), (7), (8), (9), (10), (12), (15), (16), (19), (20), or (21) or (m)(2), (4), (5), (6), or (7) of section 6103 or under section 6104(c). Any violation of this paragraph shall be a felony punishable by a fine in any amount not exceeding $5,000, or imprisonment of not more than 5 years, or both, together with the costs of prosecution.
(3) Other persons
It shall be unlawful for any person to whom any return or return information (as defined in section 6103(b)) is disclosed in a manner unauthorized by this title thereafter willfully to print or publish in any manner not provided by law any such return or return information. Any violation of this paragraph shall be a felony punishable by a fine in any amount not exceeding $5,000, or imprisonment of not more than 5 years, or both, together with the costs of prosecution.
(4) Solicitation
It shall be unlawful for any person willfully to offer any item of material value in exchange for any return or return information (as defined in section 6103(b)) and to receive as a result of such solicitation any such return or return information. Any violation of this paragraph shall be a felony punishable by a fine in any amount not exceeding $5,000, or imprisonment of not more than 5 years, or both, together with the costs of prosecution.
(5) Shareholders
It shall be unlawful for any person to whom a return or return information (as defined in section 6103(b)) is disclosed pursuant to the provisions of section 6103(e)(1)(D)(iii) willfully to disclose such return or return information in any manner not provided by law. Any violation of this paragraph shall be a felony punishable by a fine in any amount not to exceed $5,000, or imprisonment of not more than 5 years, or both, together with the costs of prosecution.
(b) Disclosure of operations of manufacturer or producer
Any officer or employee of the United States who divulges or makes known in any manner whatever not provided by law to any person the operations, style of work, or apparatus of any manufacturer or producer visited by him in the discharge of his official duties shall be guilty of a misdemeanor and, upon conviction thereof, shall be fined not more than $1,000, or imprisoned not more than 1 year, or both, together with the costs of prosecution; and the offender shall be dismissed from office or discharged from employment.
(c) Disclosures by certain delegates of Secretary
All provisions of law relating to the disclosure of information, and all provisions of law relating to penalties for unauthorized disclosure of information, which are applicable in respect of any function under this title when performed by an officer or employee of the Treasury Department are likewise applicable in respect of such function when performed by any person who is a “delegate” within the meaning of section 7701(a)(12)(B).
(d) Disclosure of software
Any person who willfully divulges or makes known software (as defined in section 7612(d)(1)) to any person in violation of section 7612 shall be guilty of a felony and, upon conviction thereof, shall be fined not more than $5,000, or imprisoned not more than 5 years, or both, together with the costs of prosecution.