No, it's not true. There is ample case law where the constitutionality of income taxes has been tested, and the courts have clearly ruled that income taxes are constitutional. Such claims are regarded as frivolous and subject to legal penalties. The IRS has a publication which clearly spells out the significant penalties for pursuing or promoting frivolous claims, and includes the following statement from the decision in one such case:
"Once the legal system has resolved a claim, judges and lawyers must move on to other things. They cannot endlessly rehear stale arguments . . . . [T]here is no constitutional right to bring frivolous suits . . . . People who wish to express displeasure with taxes must choose other forums, and there are many available."
The IRS discusses it at length in a document titled The Truth About Frivolous Tax Arguments
This document addresses numerous examples of claims that income taxes are unconstitutional and cites the case law in which courts have ruled in favor of income taxes. Some claims, and excerpts from the IRS response, include the following. All are supported by references to the actual court decisions.
First Amendment Claims:
The First Amendment, however, does not provide a right to refuse to pay income taxes on religious or moral grounds or because taxes are used to fund government programs opposed by the taxpayer. The First Amendment does not protect commercial speech or speech that aids or incites taxpayers to unlawfully refuse to pay federal income taxes, including speech that promotes abusive tax avoidance schemes.
Fifth Amendment Claims:
The Fifth Amendment to the United States Constitution provides that a person shall not be “deprived of life, liberty, or property, without due process of law . . . .” The United States Supreme Court stated that “it is . . . well settled that [the Fifth Amendment] is not a limitation upon the taxing power conferred upon Congress by the Constitution; in other words, that the Constitution does not conflict with itself by conferring, upon the one hand, a taxing power, and taking the same power away, on the other, by the limitations of the due process clause.”
There is no constitutional right to refuse to file an income tax return on the ground that it violates the Fifth Amendment privilege against self‑incrimination.
Thirteenth amendment claims:
Courts have consistently found arguments that taxation constitutes a form of involuntary servitude to be frivolous.
Sixteenth Amendment Claims:
the United States Supreme Court upheld the constitutionality of the income tax laws enacted subsequent to ratification of the Sixteenth Amendment. Brushaber v. Union Pacific R.R., 240 U.S. 1 (1916). Since that time, the courts have consistently upheld the constitutionality of the federal income tax
The constitutionality of the Sixteenth Amendment has invariably been upheld when challenged. Numerous courts have both implicitly and explicitly recognized that the Sixteenth Amendment authorizes a non‑apportioned direct income tax on United States citizens and that the federal tax laws are valid as applied.