Do a man grep on your system, and see what version you have. Your version of grep may not be able to use --exclude-dirs.
You're really better off using find to find the files you want, then use grep to parse them:
$ find . -name '.git' -type d -prune \
     -o -name "*.min.*" -prune \
     -o -type f -exec grep --color -n -H {} "$pattern" \;
I'm not a fan of the recursive grep. Its syntax has become bloated, and it's really unnecessary. We have a perfectly good tool for finding files that match a particular criteria, thank you.
In the find program, the -o separate out the various clauses. If a file has not been filtered out by a previous -prune clause, it is passed to the next one. Once you've pruned out all of the .git directories and all of the *.min.* files, you pass the results to the -exec clause that executes your grep command on that one file.
Some people prefer it this way:
$ find . -name '.git' -type d -prune \
     -o -name "*.min.*" -prune \
     -o -type f -print0 | xargs -0 grep --color -n -H "$pattern"
The -print0 prints out all of the found files separated by the NULL character. The xargs -0 will read in that list of files and pass them to the grep command. The -0 tells xargs that the file names are NULL separated and not whitespace separated. Some xargs will take --null instead of the -0 parameter.