Just google "is real ID the mark of the beast" or "is social security number the mark of the beast" like I did above.
The premillenial dispensationalism theory is widespread in southern evangelical churches in the US, with big sales of associated media.
The association is "verse says a mark will be required and a number of the beast is mentioned" -> "these are numbers assigned by the government required for commerce" -> "this is the mark." The language of the apocalopytic verses is flowery enough that people pick and choose which parts they take literally, so for a while it wasn't seen as necessarily an injection (or you could also believe that eventually you'd have to get a SSN tattoo, say).