Sorry, I also had to install AFNI on MacOS version 10.15.4 and I ran into some similar issues too. I used this page. Here is the output of the check stage:

-------------------------------- general ---------------------------------
architecture:         64bit 
system:               Darwin
release:              19.4.0
version:              Darwin Kernel Version 19.4.0: Wed Mar  4 22:28:40 PST 2020; root:xnu-6153.101.6~15/RELEASE_X86_64
distribution:         10.15.4 x86_64
number of CPUs:       20
apparent login shell: SHELL_NOT_DETECTED
shell RC file:        NONE (does not exist)

--------------------- AFNI and related program tests ---------------------
which afni           : /Users/jamie/abin/afni
afni version         : Precompiled binary macos_10.12_local: Jul  6 2018 
                     : AFNI_18.2.04
AFNI_version.txt     : AFNI_18.2.04, macos_10.12_local, Jul 06 2018
which python         : /Users/tlab/miniconda3/bin/python
python version       : 3.7.6
which R              : /usr/local/bin/R
R version            : R version 3.5.3 (2019-03-11) -- "Great Truth"
which tcsh           : /bin/tcsh

instances of various programs found in PATH:
    afni    : 1   (/Users/jamie/abin/afni)
    R       : 1   (/Library/Frameworks/R.framework/Versions/3.5/Resources/bin/R)
    python  : 4 
      /Users/tlab/miniconda3/bin/python3.7
      /Library/Frameworks/Python.framework/Versions/2.7/bin/python2.7
      /Users/jamie/anaconda3/bin/python3.6
      /System/Library/Frameworks/Python.framework/Versions/2.7/bin/python2.7
    python2 : 2 
      /Library/Frameworks/Python.framework/Versions/2.7/bin/python2.7
      /System/Library/Frameworks/Python.framework/Versions/2.7/bin/python2.7
    python3 : 4 
      /Users/tlab/miniconda3/bin/python3.7
      /Users/jamie/anaconda3/bin/python3.6
      /Library/Frameworks/Python.framework/Versions/3.6/bin/python3.6
      /usr/bin/python3


testing ability to start various programs...
    afni                 : success
    suma                 : success
    3dSkullStrip         : success
    uber_subject.py      : success
    3dAllineate          : success
    3dRSFC               : success
    SurfMesh             : success
    3dClustSim           : success

checking for R packages...
    rPkgsInstall -pkgs ALL -check : FAILURE
        
        oo Warning: 
           These packages are not installed on the computer: afex!
        These packages are not installed on the computer: lme4!
        These packages are not installed on the computer: brms!
        

checking for $HOME files...
    .afnirc                   : found
    .sumarc                   : found
    .afni/help/all_progs.COMP : found

------------------------------ python libs -------------------------------
** python module not found: PyQt4
-- PyQt4 is no longer needed for an AFNI bootcamp

-------------------------------- env vars --------------------------------
PATH = /Users/tlab/miniconda3/bin:/Users/tlab/miniconda3/condabin:/Users/jamie/mrtrix3/bin:/usr/local/opt/qt/bin:/Applications/freesurfer/bin:/Applications/freesurfer/fsfast/bin:/Applications/freesurfer/tktools:/usr/local/fsl/bin:/Applications/freesurfer/mni/bin:/usr/local/fsl/bin:/Library/Frameworks/Python.framework/Versions/2.7/bin:/Users/jamie/anaconda3/bin:/Library/Frameworks/Python.framework/Versions/3.6/bin:/Users/jamie/dinifti:/Volumes/Documents/DTI Portfolio/shell-scripts:/Users/jamie/antsbin/bin:/usr/local/spharm:/usr/local/bin:/usr/bin:/bin:/usr/sbin:/sbin:/Applications/MRIcron:/Library/TeX/texbin:/opt/X11/bin:/Users/jamie/abin

PYTHONPATH = :/Users/jamie/python/

R_LIBS = 
LD_LIBRARY_PATH = 
DYLD_LIBRARY_PATH (sub-shell) = 
DYLD_FALLBACK_LIBRARY_PATH (sub-shell) = 

------------------------------ data checks -------------------------------
data dir : found AFNI_data6   under $HOME
           top history: 20 Feb 2020 [rickr]: updated FT_analysis examples
data dir : found AFNI_demos   under $HOME
           top history: 22 Oct 2019 [discoraj]: added Cluster Explorer Demo
data dir : found suma_demo    under $HOME
           top history: ...s_New/data/Build_tmp on Mon Mar  4 11:56:45 EST 2013
data dir : found afni_handouts under $HOME
atlas    : found TT_N27+tlrc  under /Users/jamie/abin

------------------------------ OS specific -------------------------------
which brew           : /usr/local/bin/brew
brew version         : Homebrew 2.1.7

-- for PyQt4 under brew, consider running:
   brew install cartr/qt4/pyqt
++ found valid link /usr/local/lib/libglib-2.0.dylib
   to ../Cellar/glib/2.54.3/lib/libglib-2.0.dylib
++ found 1 dylib files under '/opt/X11/lib/flat_namespace'
   -- found 'libXt' dylib files:
      /opt/X11/lib/flat_namespace/libXt.6.dylib
-- recent OS X, cheating to check DYLD_LIBRARY_PATH in cur shell 'SHELL_NOT_DETECTED'...
** env var DYLD_LIBRARY_PATH not set to contain /opt/X11/lib/flat_namespace
-- recent OS X, cheating to check DYLD_LIBRARY_PATH in shell 'tcsh'...
++ found evar DYLD_LIBRARY_PATH = /opt/X11/lib/flat_namespace:/opt/X11/lib/flat_namespace

=========================  summary, please fix:  =========================
*  login shell 'SHELL_NOT_DETECTED', trusting user to translate from 'tcsh'
*  have python version 3.7.6, some programs need 2.7.x
*  missing R packages (see rPkgsInstall)
*  consider linking /usr/local/Cellar/gcc/9.1.0/lib/gcc/9/libgomp.1.dylib under /usr/local/lib
*  please set DYLD_LIBRARY_PATH to /opt/X11/lib/flat_namespace in SHELL_NOT_DETECTED

(1) I am unsure about what "SHELL_NOT_DETECTED" or how to "set DYLD_LIBRARY_PATH to /opt/X11/lib/flat_namespace in SHELL_NOT_DETECTED"
(2) Again, I installed Miniconda for both 2.7 and 3.7 but it seems to only detect 2.7?
(3) rPkgsInstall had errors with afex, lme4, and brms and I cannot install them
(4) I do not know what it means (or how to) link /usr/local/Cellar/gcc/9.1.0 etc. under /usr/local/lib

Thank you for the help with that too!