Regarding the religious folks in DTD, Pruneyard Shopping Center v. Robins, 447 U.S. 74 (1980) basically held that under the California Constitution, individuals may peacefully exercise their right to free speech in parts of private shopping centers regularly held open to the public, so long as they aren't disruptive.
This was narrowed by Ralphs Grocery Co. v. United Food and Commercial Workers Union Local 8, 55 Cal. 4th 1083 (2012), to those with areas analogous to public gathering areas such as plazas, atriums, or food courts.
My take is Disney doesn't interfere with these folks as long as they do not try to encourage people over to their displays. I've been past these tables dozens of times and not once have I ever been called to or solicited. They seem to just sit there and only engage with people who voluntarily approach them.