a workflow for binary rasterization in r

This is how you can do this better with raster. Note the value=1 argument, and also that that I changed your specification of the extent — as what you do is probably not correct.

library(raster)
v <- shapefile(shapefile_path)
ext <- extent(-180, 180, -65, 75)
r <- raster(ext, res = 1/120)
rr <- rasterize(v, r, value=1, background = 0)

There is no need for your last step, but you could have done

rr <- clamp(rr, 0, 1)
# or 
rr <- rr > 0
# or
rr <- reclassify(rr, cbind(1, Inf, 1))

raster::calc is not very efficient for simple arithmetic like this

It should be much faster to rasterize all vector data in one step, rather than in a loop, especially with large rasters like this (for which the program may need to write a temp file for each iteration).

To illustrate this solution with example data

library(raster)
cds1 <- rbind(c(-180,-20), c(-140,55), c(10, 0), c(-140,-60))
cds2 <- rbind(c(-10,0), c(140,60), c(160,0), c(140,-55))
cds3 <- rbind(c(-125,0), c(0,60), c(40,5), c(15,-45))
v <- spLines(cds1, cds2, cds3)   
r <- raster(ncols=90, nrows=45)

r <- rasterize(v, r, field=1)

To speed things up, you can use terra (the replacement for raster)

library(raster)
f <- system.file("ex/lux.shp", package="terra")
v <- as.lines(vect(f))
r <- rast(v, ncol=75, nrow=100)
x <- rasterize(v, r, field=1)