You need to make a spatial points object and then reproject __that__:

    library(sp)
    library(maptools)
    data(wrld_simpl)
    wrld_simpl.trans <- spTransform(wrld_simpl, CRS = ("+proj=moll +lon_0=0 +x_0=0 +y_0=0"))
    plot(wrld_simpl.trans, col = 'lightgray'))
    latitudes <- c(-30, 0, 20, 50)
    longitudes <- c(-20, 10, 50, 80)

Make an SPDF:
    
    pts <- data.frame(latitudes, longitudes)
    coordinates(pts) <- ~longitudes+latitudes
    proj4string(pts) <- CRS(paste("+init=epsg:4326"))

Project and plot it:
    
    pts.trans <- spTransform(pts, CRS = ("+proj=moll +lon_0=0 +x_0=0 +y_0=0"))
    points(pts.trans, cex = 1.5, col = 'red', pch = 19)

[![enter image description here][1]][1]
    
    # Compare to unprojected
    plot(wrld_simpl, col = 'lightgray')
    points(pts, cex = 1.5, col = 'red', pch = 19)

[![enter image description here][2]][2]

EDIT: This is actually a little more fun with extreme points:

    longitudes <- seq(-150, 150, length.out = 5)
    latitudes <- seq(-90, 90, length.out = 5)

[![enter image description here][3]][3]


  [1]: https://i.sstatic.net/soNOI.png
  [2]: https://i.sstatic.net/NGqsL.png
  [3]: https://i.sstatic.net/hn7ju.png