Comparing strings in a case insensitive way seems trivial, but it's not. I will be using Python 3, since Python 2 is underdeveloped here.

The first thing to note is that case-removing conversions in Unicode aren't trivial. There is text for which text.lower() != text.upper().lower(), such as "ß":

>>> "ß".lower()
'ß'
>>> "ß".upper().lower()
'ss'

But let's say you wanted to caselessly compare "BUSSE" and "Buße". Heck, you probably also want to compare "BUSSE" and "BUẞE" equal - that's the newer capital form. The recommended way is to use casefold:

str.casefold()

Return a casefolded copy of the string. Casefolded strings may be used for caseless matching.

Casefolding is similar to lowercasing but more aggressive because it is intended to remove all case distinctions in a string. [...]

Do not just use lower. If casefold is not available, doing .upper().lower() helps (but only somewhat).

Then you should consider accents. If your font renderer is good, you probably think "ê" == "ê" - but it doesn't:

>>> "ê" == "ê"
False

This is because the accent on the latter is a combining character.

>>> import unicodedata
>>> [unicodedata.name(char) for char in "ê"]
['LATIN SMALL LETTER E WITH CIRCUMFLEX']
>>> [unicodedata.name(char) for char in "ê"]
['LATIN SMALL LETTER E', 'COMBINING CIRCUMFLEX ACCENT']

The simplest way to deal with this is unicodedata.normalize. You probably want to use NFKD normalization, but feel free to check the documentation. Then one does

>>> unicodedata.normalize("NFKD", "ê") == unicodedata.normalize("NFKD", "ê")
True

To finish up, here this is expressed in functions:

import unicodedata

def normalize_caseless(text):
    return unicodedata.normalize("NFKD", text.casefold())

def caseless_equal(left, right):
    return normalize_caseless(left) == normalize_caseless(right)

>>> def cmp(a, b):
...     return [c for c in a if c.isalpha()] == [c for c in b if c.isalpha()]
... 
>>> cmp('Hai, this is a test', 'Hai ! this is a test')
True
>>> cmp('Hai, this is a test', 'Hai this is a test')
True
>>> cmp('Hai, this is a test', 'other string')
False

This creates two temporary lists, but doesn't modify the original strings in any way.

Optimizing your search will require that you don't repeat costly operations on every item if they can be performed once beforehand.

It would also help to avoid the overhead of special character processing if the search text doesn't justify it (e.g if it has no spaces or special characters itself).

Finally, procedural code (for loops) are optimized more efficiently by the compiler than their "functional" equivalent (.filter / .map) so the traversal of songs should be performed in a loop instead of a .filter()

I would suggest extending the MPMediaQuery class to allow it to provide a filtered list of songs in the most optimal way possible. This has some reuse value and will keep your main logic more readable and maintainable.

On the other hand, if the MPMediaQuery goes back to storage every time, it will be more efficient to create a simple function that takes the array of songs as a parameter.

For example:

extension MPMediaQuery
{
   static func songsMatching(_ searchText:String) -> [MPMediaItem]
   {
      // Common function to turn special characters into spaces
      // will have a certain amount of overhead so we will try
      // to avoid using it if possible...
      func normalizedText(_ text:String) -> String
      {
         let chars = text.unicodeScalars.enumerated()
                         .map ({ 
                                   CharacterSet.punctuationCharacters.contains($1)
                                || CharacterSet.whitespaces.contains($1) 
                                   ? " " : Character($1)
                              })
         return String(chars)
      }

      // Search string should only be prepared once
      // This means that the whole filtering operation needs to be
      // included in the optimization.
      let searchString  = searchText.lowercased()      
      let cleanedString = normalizedText(searchString)

      // based on search string content, we can forgo complex comparisons
      // We only need to manage special characters if the search text
      // contains any.
      // If the search text doesn't contain spaces or special characters
      // then removing them from the titles is unnecessary
      let simpleFilter = !cleanedString.contains(" ")

      // The Swift optimizer is much more efficient compiling procedural
      // code (As opposed to the functional style .filter{} and such)
      // This can give a 20x speed boost in some cases.
      var result:[MPMediaItem] = []
      for song in songs().items ?? []
      {
         guard let title = song.title?.lowercased()
         else { continue }

         if simpleFilter
         { 
            if title.contains(searchString)
            { result.append(song) }
         }
         else
         {
            if normalizedText(title).contains(searchString)
            { result.append(song) }
         }
      }

      return result
  }    
}

In bash, you can use a parameter expansion syntax to take the value of a variable with some characters removed (or more generally replacing occurrences of a pattern).

if [[ "${a//[$' \t\n\r']/}" == "${b//[$' \t\n\r']/}" ]]; then
  echo ok
fi

If the problem is that they're “using different newline characters”, that probably means that one of them is coming from a Windows file. Windows lines have an extra CR (carriage return, $'\r in bash syntax) before the newline character ($'\n'). If you have multiline strings, you can strip off just the CR characters:

if [[ "${a//$'\r'/}" == "${b//$'\r'/}" ]]; then
  echo ok
fi

If the variables are single-line strings then the troublesome CR would be at the end and you can use the suffix stripping syntax:

if [[ "${a%$'\r'}" == "${b%$'\r'}" ]]; then
  echo ok
fi

If you need this one in plain sh, the (minor) difficulty is entering a CR character.

cr=$(printf '\r')
if [[ "${a%$cr}" == "${b%$cr}" ]]; then
  echo ok
fi

You could use a regex:

import re

st="Money is the last money."

words=st.split()
beats=['money','nonsense']

for i,word in enumerate(words):
    if word=='match': continue
    for tgt in beats:
        word=re.sub(r'\b{}\b'.format(tgt),'match',word,flags=re.I)
        words[i]=word

print print ' '.join(words)    

prints

match is the last match.