If that were the issue, it's not racist. The response isn't based on the speaker's race but on the content. But it arguably could be 'jumping to a conclusion'.
But I don't think it's that either. The comment said that such statements are often thinly-veiled racism, which is true. Racism is infrequently expressed literally; there is a lot of 'dog whistle' communication and policies. For example, there's a semi-famous interview with a Republican strategist who said that, during the Reagan years, they realized they could no longer make outright racist statements, so they adopted school busing as an issue and expected that everyone would get the message - they couldn't outright say, 'you don't want your kids going to school with black kids, and we're the party that will stop that kind of thing', but they could talk about busing.
Today, when Republican state governments take away voting locations in minority areas, and create ID and registration requirements that disproportionately affect minorities, it's pretty thinly veiled. In fact, those are some of the same tactics were used before the Voting Rights Act (the tactics returned immediately after Republicans on the U.S. Supreme Court invalidated parts of the Act). Some Republicans openly say that it's to prevent Democrats from voting.