Many employers are averse to adopting pre-hire assessments; they consider them to be introducing additional litigation and compliance risks to their hiring process.

This is a common misconception; in fact, when reviewing federal court cases, one will find almost four times as many court cases challenging Interview practices than pre-hire assessment practices.

In this context adverse and disparate are used interchangeably.
Adverse treatment is intentional employment discrimination. For example, a requirement for a college degree that applies only to Latinx.
Adverse impact is unintentional employment discrimination. For example, a requirement for a college degree constitutes adverse impact.

This means that most job postings out there with a college degree requirement (or even a prior experience requirement) run afoul of EEOC regulations. Luckily this is not the case, because unlike adverse treatment (which is always prohibited), selection procedures with an adverse impact are allowed when they are justified (UGESP § 1607.3.A and Title VII). 

Justified in this context means that the selection process results are related to the performance of the role in question and that no other, better selection process is known. For example, a French-language assessment would not be justified for all Sales roles in a company; it would be justified for those roles that are specifically targeting French-speaking customers.

There is ample evidence in I/O Psychology research that a combination of cognitive skills and personality traits in an assessment is the best predictor of future job performance. (For example, see Schmidt, Frank & Hunter, John. (1998). The Validity and Utility of Selection Methods in Personnel Psychology. Psychological Bulletin. 124. 262-274. 10.1037/0033-2909.124.2.262.).

Furthermore, UGESP § 1607.14 determines the Technical standards for validity studies, which are available for Bryq.

Finally, Bryq represents an objective set of standardized criteria used for hiring, both in terms of selection and interviewing. It has been shown that the usage of systems, such as Bryq, which contribute to enhanced reliability and validity, are also viewed by the courts as enabling the interview to protect against unlawful employment discrimination (Williamson, L. G., Campion, J. E., Malos, S. B., Roehling, M. V., & Campion, M. A. (1997). Employment interview on trial: Linking interview structure with litigation outcomes. Journal of Applied Psychology, 82(6), 900–912.). 

Regardless of the hiring and selection process you are using, you should be measuring the adverse impact your practices have in hiring.
Using an objective tool, such as Bryq, also usually improves these metrics, as it removes common unconscious bias factors typical in resume screening (such as name, gender, age, education and more) from the equation.

This article does not constitute legal advice, but is designed to help you understand and deal with these issues.

SHRM Avoiding (and measuring) adverse impact
Uniform Guidelines on Employee Selection Procedures
EEOC Fact Sheet on Employment Tests and Selection Procedures