The term was and is so common it won't raise suspicions of racial connotations among lawyers. It's useful to distinguish between other historical legal traditions that entered the American system. Louisiana and Puerto Rico are dual systems, for example, incorporating civil law traditions which don't have British roots. The community property regimes of most southwestern states are holdovers from Mexican inheritance regimes which treated marital property differently than the Anglo-American tradition. Due to the conservative nature of legalese, the law often has anachronistic meanings assigned to words which don't mesh with their current connotations.

My favorite example of a legal anachronism was the continued use of the word "concubine" to distinguish between a common law wife and live in girl-friends. "Common-law marriages do exist. Concubinage also exists." State v. Lawson, 165 NW 2d 838 - Iowa: Supreme Court 1969.

The 9th and 10th Amendments are generally understood to have incorporated the English Common Law as it existed in the colonies before the Revolutionary War, after which point the traditions split and evolved in different directions. Still, the machinery of a common law court is fundamentally distinguishable from Latin American or Continental legal systems. For example, the Anglo-American system is adversarial, rather than inquisitorial. In the Anglo American tradition, lawyers rather than judges play the leading roles in discovering and presenting evidence. Common law judges don't conduct the direct and cross examination of the witnesses, the lawyers do. You may have seen movies of inquisitorial systems where the witnesses or accused are brought before the Court and stand in front of the judge answering the judge's questions, such as Les Miserables. That wouldn't happen in the Anglo-American tradition.

After the Revolution, the English and American common law evolved independently, especially along the lines of judge made law. In America, for example there is an exclusionary evidence rule, meaning evidence obtained in violation of the 4th and 5th Amendment gets excluded from the jury. Even in England, the accused doesn't receive a get out of jail free card for police malfeasance, but if they find the body in your trunk without a warrant, America (hypothetically) can't use it as evidence. There are too many examples to go over in detail, but basically western legal traditions are a tree with its roots in Rome, the breaking into common law (English) and civil law (Napoleonic Code) traditions, and spreading out into various national branches from there.

As some final illustration of the banality of the word "Anglo-American" in jurisprudence, here is a list of quotes showing the Supreme Court's historic use of the term:

"The underlying idea, one that is deeply ingrained in at least the Anglo-American system of jurisprudence, is that the State with all its resources and power should not be allowed to make repeated attempts to convict an individual for an alleged offense, thereby subjecting him to … " (1957)

"The recent cases, on the other hand, have proceeded upon the valid assumption that state criminal processes are not imaginary and theoretical schemes but actual systems bearing virtually every characteristic of the common-law system that has been developing contemporaneously in England and in this country. The question thus is whether given this kind of system a particular procedure is fundamental—whether, that is, a procedure is necessary to an Anglo-American regime of ordered liberty. " (1968)

"The existence of a mens rea is the rule of, rather than the exception to, the principles of Anglo-American criminal jurisprudence." (1950)

"It is a principle of general application in Anglo-American jurisprudence that one is not bound by a judgment in personam in a litigation in which he is not designated as a party" (1940)

"serves the purposes of the Confrontation Clause by ensuring that evidence admitted against an accused is reliable and subject to the rigorous adversarial testing that is the norm of Anglo-American criminal proceedings " (1990)

"The established safeguards of the Anglo-American legal system leave the veracity of a witness to be tested by cross-examination, and the credibility of his testimony to be determined by a properly instructed jury" (1960)

"Since under the procedures of Anglo-American criminal justice they cannot be constrained by legal process to give answers which incriminate them," (1961)

Cases: https://scholar.google.com/scholar?hl=en&as_sdt=4%2C60&q=Anglo-American&oq=