is there any way to exploit input() and make it output "RIGHT password"?

Yep:

C:\Users\Kevin\Desktop>py -2 test.py
Enter the password: __import__('sys').stdout.write('RIGHT password') or exit(0)
RIGHT password
C:\Users\Kevin\Desktop>

"But that doesn't count because you're printing your own output and terminating early", you protest hypothetically. "Show me an example where the conditional actually executes".

C:\Users\Kevin\Desktop>py -2 test.py
Enter the password: (1, globals().update({"random": type("", (object,), {"__init__": lambda self: setattr(self, "randint", lambda x,y: "1")})()}))[0]
RIGHT password

C:\Users\Kevin\Desktop>

"Ok, well, in a real application I wouldn't be using random.randint to determine the password. Show me an example where the conditional inp == "hunter2": passes"

import random
inp = str(input("Enter the password: "))
if inp == "hunter2":
    print "RIGHT password" 
else:
    print "WRONG password"

C:\Users\Kevin\Desktop>py -2 test.py
Enter the password: __import__("re").search(r"if inp == \"(.*?)\"", open(__file__).read()).group(1)
RIGHT password

"That doesn't count because you read the file. Show me an example where you don't extract the password from the source code"

C:\Users\Kevin\Desktop>py -2 test.py
Enter the password: type("", (str,), {"__str__": lambda self: self, "__eq__": lambda self, other: True})()
RIGHT password

C:\Users\Kevin\Desktop>

Approach 1: Overriding random.randint() Completely

Assuming the interpreter is Python 2, the following input will cause the result of the comparison to be True, without modifying the program at all:

[42 for random.randint in [lambda x,y: 42]][0]

Witness the execution transcript:

$ python test.py
What is the password?[42 for random.randint in [lambda x,y: 42]][0]
Access granted.

Digression: How It Works

To explain this -- in Python 2, input() -- as opposed to raw_input() -- runs content entered by the user through an evaluation pass. This means code can access defined variables, or have side effects on them.

lambda x,y: 42

is a function that takes two arguments, and always returns 42.

[42 for random.randint in [lambda x,y: 42]]

is a list comprehension that goes through a list of items containing only that lambda expression, assigning each of them in turn to the variable random.randint, and then adding the value 42 to its list; tacking on a [0] on the end thus makes the end effect be an evaluation to that value.

Approach 2: Setting a Known Seed

[random.seed(1), random.randint(0, 2**30), random.seed(1)][1]

Again, the transcript:

$ python test.py
What is the password?[random.seed(1), random.randint(0, 2**30), random.seed(1)][1]
Access granted.

In this case, we caused the random number generator to be initialized with a known seed; generated a value from the same range; and then reinitialized from that seed again -- and return the second value from that list, corresponding with the first random number generated with the given range and the given seed.