While conservatives are generally not overly concerned with racism and have been willing to tolerate the racism of their fellows, they delight in an opportunity to accuse a Democrat of racism. If this Democrat also happens to be a woman and Muslim, so much the better.
This sort of attack is probably quite satisfying. First, there is the obvious value in scoring political points against Democrats. Second, it is no doubt pleasant to be able to accuse the Democrats of the very sin that they delight in laying at the feet of conservatives. Third, such attacks provide cover for the racism of certain conservatives: how dare the Democrats attack, for example, Trump for being a racist when they have racists among them? There is certainly irony in attacking Democrats for alleged racism in order to protect racists. This is not to say that racist Democrats should get a pass, but this tactic is based on a fallacy.
The most recent incident involves Democrat Ilhan Omar. Omar has been quite critical of Israel and its influence over American politics via its lobbying efforts. Unfortunately for the Democrats, but fortunately for the Republicans, she made use of terms like “hypnotize” and “allegiance” that can be interpreted as linking to anti-Semitic tropes. Her words are clearly not overtly anti-Semitic; one must interpret them through the lens of these tropes. If she had said the same words about another country, they would seem innocuous. For example, her use of “allegiance” was taken as referring to anti-Semitic conspiracy theories. However, if she had accused Trump of having an allegiance to Russia, this would obviously not be anti-Semitic.
An obvious concern, which has been raised by others, is that any criticism of Israel can easily be cast as anti-Semitism by analyzing every word of the criticism to find some connection to anti-Semitism. Even if a critic is scrupulous in their word choices, it would still be quite easy to make an accusation of anti-Semitism. For example, any criticism of the influence of Israel lobbying congress using money can easily be cast as an anti-Semitic attack based on stereotypes of Jews, money and conspiracies.
Interestingly, critics of Israel find themselves in the sort of scenario that many conservatives complain bitterly about: that their non-racist words and actions are wrongly interpreted as racist. More generally, this is the complaint about political correctness and not being able to “say things” anymore. Oddly enough, conservatives do not seem to be rushing to defend Omar from political correctness. To illustrate, when a conservative makes a monkey reference involving a black person, their defenders will profess ignorance of the racist monkey trope and assert that the person was using the reference in a perfectly non-racist manner.
While the lamentations of conservatives about political correctness can be veiled defenses of racism and sexism, their concerns do contain some merit—a person’s words can be wrongly taken as racist, especially when people are hypersensitive and are actively trying to interpret the words as racist. It can also be the case that almost any criticism can be seen as racist. For example, criticism of Obama was sometimes cast as racist, even when it would be odd to make that interpretation. As such, there is a real problem here: if criticizing a black person must be racist and criticizing Israel must be anti-Semitic, then there would be no way to offer legitimate criticism. It is obviously absurd to think that Obama or Israel should be exempt from criticism because such criticism must be racist or anti-Semitic. There are obviously many legitimate criticisms of both. As such, it would be absurd to dismiss such criticism as automatically racist. So, criticizing Israel is no more automatically anti-Semitic than criticizing Obama is automatically racist or criticizing Elizabeth Warren is sexist.
There is, however, the problem of the opposite extreme: that having some basis for legitimate criticism entails that the criticism is not racist. For example, while there are legitimate grounds to criticize Israeli influence over congress, couching this criticism in terms of an international Jewish conspiracy and remarking that Jews are the secret bankers controlling America would be anti-Semitic. As such, criticizing Israel can be anti-Semitic.