Let's assume for PF&M on-topic rules that you are asking if you must provide your birthdate to an employer for the employer's tax compliance when you are working as an employee or a contractor.
If you are a contractor (a non-employee), you must fill out a W-9 and submit it to the employer, and the employer provides a 1099 to you. Neither form has a space for date of birth, just name, address and taxpayer ID number.
If you are an employee, you must fill out a W-4 and submit it to the employer, and the employer provides a W-2 to you. Neither form has a space for date of birth, just name, address and social security number.
So in either case, the employer does not need date of birth for tax compliance.
However, all employers in the U.S. must positively identify every new employee in order to fill out an I-9 for U.S. Citizenship and Immigration Services and retain it on file. Every form of acceptable identification document includes date of birth, and the employer must inspect the original government issued ID.
So although the employer doesn't need date of birth for tax purposes, they will need it for work authorization.
In addition, there are numerous federal and state laws governing minimum age for employment in certain industries and in certain job functions, so perhaps this has some bearing on the payroll company's request for date of birth. If you submit an industry code when you set up payroll, the software or the payroll company may alert you that a person is under-age for this industry.