Find -exec not working in fish

As for the find command, you can also just add more -exec commands in a row:

find . -name "*" -exec chgrp -v new_group '{}' \; -exec chmod -v 770 '{}' \;

Note that this command is, in its result, equivalent of using

chgrp -v new_group file && chmod -v 770 file

on each file.

All the find's parameters such as -name, -exec, -size and so on, are actually tests: find will continue to run them one by one as long as the entire chain so far has evaluated to true. So each consecutive -exec command is executed only if the previous ones returned true (i.e. 0 exit status of the commands). But find also understands logic operators such as or (-o) and not (!). Therefore, to use a chain of -exec tests regardless of the previous results, one would need to use something like this:

find . -name "*" \( -exec chgrp -v new_group {} \; -o -true \) -exec chmod -v 770 {} \; 

There was several issues with your attempts, including backticks used instead of quotes (removed in later edits to the question), missing quotes where they are required, extra quotes where they are useless, missing parentheses to group -o clauses, and different implementations of findused (see the comments and chat for details).

Anyway, the command can be simplified like this:

find a/folder b/folder -name "*.[ch]" -exec grep -I foobar {} +

or, should you use an archaic GNU find version, this should always work:

find a/folder b/folder -name "*.[ch]" -exec grep -I foobar {} \;