If you have unique values in your list:

my_list[my_list.index('old_word')]='new_word' 

Looping over the items of invalid_list is inefficient. This increases the complexity of the algorithm.

An efficient solution would be to use a regex to search motifs in each string only once:

s = ['123xyz', '456xye','789xyf']

invalid_list = ['xye','xyf']

import re

regex = re.compile('|'.join(map(re.escape, invalid_list)))

s2 = [regex.sub('xyz', x) for x in s]

Output:

['123xyz', '456xyz', '789xyz']

avoid matching partial words:

s = ['123xyz', '456xye','789xyf']
invalid_list = ['xy','xye','xyf']
import re
regex = re.compile(f"({'|'.join(map(re.escape, invalid_list))})\b")
s2 = [regex.sub('xyz', x) for x in s]
# ['123xyz', '456xye', '789xyf']

Try re.sub with custom function:

import re

lst = ["text", "be", "there"]
text = "This is an example [word]. Normally there would [word] something important here but [word] isn't."


text = re.sub(r"\[word\]", lambda _, i=iter(lst): next(i), text)
print(text)

Prints:

This is an example text. Normally there would be something important here but there isn't.

try this:

prohibitedWords = ["MVGame","Kappa","DatSheffy","DansGame","BrainSlug","SwiftRage","Kreygasm","ArsonNoSexy","GingerPower","Poooound","TooSpicy"]

themessage = str(word[1])    
for word in prohibitedwords:
    themessage =  themessage.replace(word, "(I'm an idiot)")

print themessage

To filter your output you can f.e. use a simple if condition on a all-lowercase 'madrid':

students = [
    ('Marcos', 23, 'Madrid', 850, '2388711341'),
    ('Elena', 35, 'MaDrid', 360, '0387700342'),
    ('Carmen', 21, 'Getafe', 50, '0014871388'),
    ('Carlos', 41, 'MAdrid', 580, '00887118456'),
    ('Maria', 28, 'Madrixx', 150, '587')
]


for item in students:
    # decompose the item into its parts - this also fixes your NameError
    student, age, town, debt, something = item

    # use the decomposed variables instead of item[.]
    # make town all lowercase and compare - only print if matches
    if town.lower() == "madrid":
        print(f'The user {student} lives in {town.title()}, has an age of '
              f'{age} and its debt is: {debt} EUR.')

Output:

# if you simply print town
The user Marcos lives in Madrid, has an age of 23 and its debt is: 850 EUR.
The user Elena lives in MaDrid, has an age of 35 and its debt is: 360 EUR.
The user Carlos lives in MAdrid, has an age of 41 and its debt is: 580 EUR.

# with town.title()
The user Marcos lives in Madrid, has an age of 23 and its debt is: 850 EUR.
The user Elena lives in Madrid, has an age of 35 and its debt is: 360 EUR.
The user Carlos lives in Madrid, has an age of 41 and its debt is: 580 EUR.

@marmeladze pointed out I missed Maria, who seems to be incapable of using her correct town-name - you can mitigate her inabilities by using:

if "madrid".startswith(town.lower()[:4]):

instead of

if town.lower() == "madrid":

to get an output of:

The user Marcos lives in Madrid, has an age of 23 and its debt is: 850 EUR.
The user Elena lives in Madrid, has an age of 35 and its debt is: 360 EUR.
The user Carlos lives in Madrid, has an age of 41 and its debt is: 580 EUR.
The user Maria lives in Madrixx, has an age of 28 and its debt is: 150 EUR.

I just hope you never get anybody from 'Madravingpeopletown' into your list - they would show up as well...

The code you have posted doesn't actually do any replacement. Here is a snippet that does:

for key,word in enumerate(data):
   if word in unique_words:
       data[key] = replacement

Here's a more compact way:

new_list = [replacement if word in unique_words else word for word in big_list]

I think unique_words is an odd name for the variable considering its use, perhaps it should be search_list?

Edit:

After your comment, perhaps this is better:

from collections import Counter
c = Counter(data)
only_once = [k for k,v in c.iteritems() if v == 1]

# Now replace all occurances of these words with something else

for k, v in enumerate(data):
    if v in only_once:
        data[k] = replacement