The key constituency to which Rosa Parks was able to appeal were "Disadvantaged Democrats"—a heavily black and poor voting group. These folks are also more opposed to immigration than any major GOP voting group.
I'm a VDARE.com contributor, but I consider myself a leftist. I'm against open borders immigration policy because I think it is overwhelmingly a policy of transfer of assets from poorer and middle class Americans to the wealthy in the US and elsewhere
The net benefits to immigrants themselves are minor compared to these other transfers—and irrelevant to the formation of US immigration policy.
I favor expropriation via taxation of the assets the rich in the US have obtained via open borders—a stand which may be in a practical sense more threatening to the wealthy than anything Ms. Parks advocated. I think part of the reason why open borders returned to the US was that the failure of FDR to fully defang the rich via direct taxation of concentrated wealth allowed them to ramp up such policies again.
I'm not sure what Parks' stands were exactly. I suspect that the bulk of the funding for her beatification came from white, pro-immigration liberals who feared some of the other options that might develop in the black community (i.e. Black Nationalists like the Nation of Islam —or real leftists like A. Philip Randolph.) Those Liberals also wanted a highly-centralized national policy on stuff like integration.
The thing is, lots of folks loved this lady—if you want to criticize her on VDARE.com, it ought to be well researched. When you criticize her for simply being a leftist, you make it that much harder to create the types of alliances necessary to contain the class warfare-and general madness-of open borders.