Maybe it's necessary to point out that you are using Anaconda3 and a conda environment, this usually brings this kind of problems, I hope some one else with a similar setup has a solution for this, other than using a regular r/rstudio setup.
is too old to have a package for newer versions of Gdal. In this case the package is not coming from Anaconda but the CRAN mirror and the package management in R (or Python for that matter) is notoriously bad for external dependencies - especially on older Linux. Anaconda uses a rather crude method to mitigate that but the package has to come from a conda channel (so you'd install it using conda install from command line. That would download the additional gdal shared library and inject the path to your LD_LIBRARY_PATH). I don't know if conda's support for R packages matches the one for Python's though. As I've said a few times on this forum, in my case we got tired of this problem of maintaining external dependencies by hand (about 900 R packages from CRAN, Bioconductor, Github,... to manage, keep up to date, etc.). See my old post which happens to deal with Gdal. Note that our approach is not for everybody - the learning curve is rather steep.
@alexv Agreed. I understand what you mean and I have experienced similar issues with a couple of packages in the past. I already tried installing r-rgdal via conda like this: conda install -c conda-forge r-rgdal -n <env_name> but that results in either _r-mutex conflict or r-base conflict errors.
@aniketkul I know exactly what you mean - conda is brittle and unpredictable. @jlacko That's exactly what I was doing in the beginning - compiling all the missing dependencies. Until I had do build gcc from scratch (The one in RHEL 6 wasn't fully c++11 compliant but some R package wanted that). Then I decided I'd had enough.