People have been saying this for thousands of years, though. In some cases, they weren't even wrong to think it. But for a country as wealthy and well insulated and exhaustively policed as the average Western state?
Come on. We don't even have COVID era crime rates, much less the lead /cocaine fueled crime bonanzas of the 1970s and 80s.
Relative to what? The Great Depression? The Civil War? The collapse of the Aztec Empire?
Climate refugees are going to turn the "migrant crime" rhetoric into overdrive. My opinion, but it's clearly the Boogeyman that Fascism is rallying against. There are great swaths of land that are experiencing temperatures and severe weather that are incompatible with human life.
Fascists don't have the foresight to think of consequences of climate change. They're also in denial that climate change is a thing at all, since one of their sources of funding is fossil-fuel extractors, including a certain large Eurasian nation-state.
Their real motivation for being anti-immigrant is that they are racist scum who are always looking for vulnerable populations to victimise.