That is a strict constructionist view which is widely and appropriately mocked.
English common law informs literally every word of the constitution. "The People" are the demos. dêmos (δῆμος): “ordinary citizens, common people from a district, in a city-state.” It never included tourists. Also, the Privileges or Immunities Clause explicitly concedes that citizens have both privileges and immunities. Why would that be?
>It would be inappropriate, however, to require every statutory exclusion of aliens to clear the high hurdle of "strict scrutiny," because to do so would "obliterate all the distinctions between citizens and aliens, and thus depreciate the historic values of citizenship." Mauclet, supra at 432 U. S. 14 (BURGER, C.J., dissenting). The act of becoming a citizen is more than a ritual, with no content beyond the fanfare of ceremony. A new citizen has become a member of a Nation, part of a people distinct from others. Cf. 31 U. S. Georgia, 6 Pet. 515, 559 (1832). The individual, at that point, belongs to the polity, and is entitled to participate in the processes of democratic decisionmaking. Accordingly, we have recognized "a State's historical power to exclude aliens from participation in its democratic political institutions, as part of the sovereign's obligation "to preserve the basic conception of a political community.'" 413 U.S. at 413 U. S. 647.
Foley v. Connelie, 435 U.S. 291 (1978)
This means that there need not be a compelling government interest to justify discriminating between citizens and non-citizens. Nor need the discrimination be done via the least restrictive means available. At least not in the general case.