Strange library problem with 4.0

I installed R 4.0 on 2 machines, an iMac and a Macbook Pro.
Before that, I installed RSwitch and did what the site tells to do:
sudo pkgutil --forget org.r-project.R.el-capitan.fw.pkg \
             --forget org.r-project.x86_64.tcltk.x11 \
             --forget org.r-project.x86_64.texinfo \
             --forget org.r-project.R.el-capitan.GUI.pkg
so that the 3.6 and 4.0 can coexist.

I always keep the additionally installed packages in
~/Library/R

After installing R 4.0 I therefore have
~/Library/R/3.6/library and ~/Library/R/4.0/library

On the iMac, I can switch between the two versions and R will put the appropriate folder 
in .libPaths()

On the Macbook, however, when I run R 4.0
both these folders are in .libPaths().
This does not happen when I run R 3.6.

How can this problem be solved?

Erich