tldr; lose the source, use the dot (.)
Longer explanation follows...
It doesn't work because make is looking for a source program in the $PATH. This fails because source is a (non-POSIX) shell builtin, not an executable program on any conventional UNIX-like system.
I was able to replicate failure shown in the question; the following (much abridged) output was generated on Ubuntu 16.04 with GNU Make v4.1:
$ strace -f -s65536 -- make dev 2>&1 | grep 'authenticate'
read(3, "test:\n\tpytest -s\n\ndev:\n\tsource ./bin/authenticate.sh\n", 4096) = 53
write(1, "source ./bin/authenticate.sh\n", 29source ./bin/authenticate.sh
[pid 32100] execve("/usr/local/sbin/source", ["source", "./bin/authenticate.sh"], [/* 82 vars */]) = -1 ENOENT (No such file or directory)
[pid 32100] execve("/usr/local/bin/source", ["source", "./bin/authenticate.sh"], [/* 82 vars */]) = -1 ENOENT (No such file or directory)
[pid 32100] execve("/usr/sbin/source", ["source", "./bin/authenticate.sh"], [/* 82 vars */]) = -1 ENOENT (No such file or directory)
[pid 32100] execve("/usr/bin/source", ["source", "./bin/authenticate.sh"], [/* 82 vars */]) = -1 ENOENT (No such file or directory)
[pid 32100] execve("/sbin/source", ["source", "./bin/authenticate.sh"], [/* 82 vars */]) = -1 ENOENT (No such file or directory)
[pid 32100] execve("/bin/source", ["source", "./bin/authenticate.sh"], [/* 82 vars */]) = -1 ENOENT (No such file or directory)
You can see that make made six failed attempts to find the source program; i.e., one for each component of my $PATH.
If source is changed to ., make changes its strategy; instead of trying to find and execute a program, it just passes the rule body to the system shell:
$ strace -f -s65536 -- make dev 2>&1 | grep 'authenticate'
read(3, "test:\n\tpytest -s\n\ndev:\n\t. ./bin/authenticate.sh\n", 4096) = 48
write(1, ". ./bin/authenticate.sh\n", 24. ./bin/authenticate.sh
[pid 32122] execve("/bin/sh", ["/bin/sh", "-c", ". ./bin/authenticate.sh"], [/* 82 vars */]) = 0
[pid 32122] open("./bin/authenticate.sh", O_RDONLY) = 3
The kind of shell used by make determines which shell builtins get expanded within each Makefile rule. You can tell make to use a shell of your choosing like so:
$ cat Makefile
SHELL = /bin/bash
test:
pytest -s
dev:
source ./bin/authenticate.sh
Since bash defines the builtin source as a synonym for ., the rule using source now succeeds:
$ strace -f -s65536 -- make dev 2>&1 | grep 'authenticate'
read(3, "SHELL = /bin/bash\ntest:\n\tpytest -s\n\ndev:\n\tsource ./bin/authenticate.sh\n", 4096) = 71
write(1, "source ./bin/authenticate.sh\n", 29source ./bin/authenticate.sh
[pid 32573] execve("/bin/bash", ["/bin/bash", "-c", "source ./bin/authenticate.sh"], [/* 82 vars */]) = 0
[pid 32573] open("./bin/authenticate.sh", O_RDONLY) = 3
References: