st_intersection to spatialpolygon dataframe not working - r

Question

I am trying to get the intersection of two shapefiles (census tracts that fall within the boundaries of certain metropolitan areas). I am able to successfully get the intersecting features, however when I try to convert the output of sf_intersect to a SpatialPolygonsDataframe I get the error:
"Error in as_Spatial(from) : conversion from feature type
sfc_GEOMETRY to sp is not supported"
This is my code:
library(sf)
library(dplyr)
library(tigris)
library(sp)
#download shapefiles corresponding to metro areas
metro_shapefiles<-core_based_statistical_areas(cb = FALSE, year = 2016)
#convert to sf and filter
metro_shapefiles<-st_as_sf(metro_shapefiles)%>%filter(GEOID==31080 )
#Data for California
census_tracts_california<-tracts(state="CA",year=2016)
census_tracts_california<-st_as_sf(census_tracts_california)
#INTERSECT AND CONVERT BACK TO SP
census_tracts_intersected1<-st_intersection(census_tracts_california,
metro_shapefiles)
#back to spatial
census_tracts_intersected1<-as(census_tracts_intersected1,"Spatial")

Answer 1

The error message is telling you you can't convert an sfc_GEOMETRY to a Spatial object. There is no sp equivalent object.
In your intersection result you have a mixture of geometries (and hence, you're returned an sfc_GEOMETRY as your 'geometry'). You can see all the geometries here:
types <- vapply(sf::st_geometry(census_tracts_intersected1), function(x) {
class(x)[2]
}, "")
unique(types)
# [1] "POLYGON" "MULTILINESTRING" "MULTIPOLYGON"
If you want, you can extract each type of geometry, and convert those to SP individually:
lines <- census_tracts_intersected1[ grepl("*LINE", types), ]
polys <- census_tracts_intersected1[ grepl("*POLYGON", types), ]
spLines <- as(lines, "Spatial")
spPolys <- as(polys, "Spatial")
Additional Information
I mentioned in the comments you could use st_join. However, this may not give you the result you want. Within sf library there are the geometric binary predicates, such as ?st_intersects, and geometric operations such as ?st_intersection
The predicates return a sparse (default) or dense matrix telling you with which geometry of y each geometry of x intersects. If you use this within st_join, it will return the (original) geometries that intersect, rather than the sparse matrix.
Whereas the operations (e.g. st_intersection) will compute the intersection, and return new geometries.
Example use
The predicates (st_intersects) can be used inside st_join, and they will return the original geometries which 'intersect'
sf_join <- sf::st_join(census_tracts_california, metro_shapefiles, join = st_intersects)
In this case this gives a single type of object
types <- vapply(sf::st_geometry(sf_join), function(x) {
class(x)[2]
}, "")
unique(types)
# [1] "MULTIPOLYGON"
## so you can convert to a Spatial object
spPoly <- as(sf_join, "Spatial")
But you need to decide if the result of st_intersect is what you're after, or whether you need the new geometries given by st_intersection.
Further reading
information on each join is on the sf blog.
spatial predicates and examples of what the different operations do are on wikipedia (with some good illustrations)
Credit to user #lbussett for their description on the difference between st_intersect and st_intersection

Answer 2

Conversion to a Spatial object can't handle mixed lines and polygons. After the intersection you can extract just the polygons (and discard any lines) using:
st_collection_extract("POLYGON")
Your example doesn't seem to fail anymore, so I've created a new example that intersects two polygons, with a shared side. This results in an intersection output of a polygon and a line.
On the second attempt I've piped the intersection through the st_collection_extract() function prior to successful conversion to a Spatial object.
library(sf)
library(dplyr)
library(sp)
#Create some boxes
BoxA <- st_polygon(list(cbind(c(0,0,2,2,0),c(0,2,2,0,0))))
BoxB <- st_polygon(list(cbind(c(1,1,3,3,1),c(1,3,3,1,1))))
BoxC <- st_polygon(list(cbind(c(2,2,4,4,2),c(0,2,2,0,0))))
#Create a funny shaped union to help demonstrate the intersection issue
BoxAB <- st_union(BoxA,BoxB)
plot(BoxAB)
plot(BoxC,add=TRUE,border="blue")
Example polygons to intersect
#Intersect of BoxAB with BoxC results in a line and a polygon
BoxIntersects<-st_intersection(BoxAB,BoxC)
plot(BoxIntersects)
Intersection made up of a polygon and a line
#back to spatial fails
SpatialVersionOfIntersects<-as(BoxIntersects,"Spatial")
Error in .as_Spatial(from, cast, IDs) :
conversion from feature type sfc_GEOMETRY to sp is not supported
#Intersect again, but this time extract only the polygons
BoxIntersects<-st_intersection(BoxAB,BoxC) %>% st_collection_extract("POLYGON")
#back to spatial suceeds!
SpatialVersionOfIntersects<-as(BoxIntersects,"Spatial")