Ranges in the pattern syntax use the sorting rules of your collation.

Use a binary collate clause so the range is ordered by character code.

(I also changed it to `LIKE` as I find that more obvious than `PATINDEX > 0`)

    SELECT *
    FROM mbrnotes
    WHERE LINE_TEXT COLLATE Latin1_General_100_BIN2 
         LIKE '%[' + CHAR(0)+ '-' +CHAR(31) + CHAR(127)+ '-' +CHAR(255)+']%'  

If you actually want to see the offending characters and you are on a version with the `TRANSLATE` function you can use something like the below

    DECLARE @WhiteListedCharacters NVARCHAR(1000)
    = ' !"#$%&''()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ'
    + '[\]^_`abcdefghijklmnopqrstuvwxyz{|}~'
    
    SELECT text,
        REPLACE(
            TRANSLATE(
                text,
        	    @WhiteListedCharacters COLLATE Latin1_General_100_BIN2, 
        		REPLICATE(
                    LEFT(@WhiteListedCharacters,1),
                    LEN(@WhiteListedCharacters))), 
        	LEFT(@WhiteListedCharacters,1), 
        	'') AS BadChars
    FROM   sys.messages
    WHERE  language_id = 1038 


You can then use that result in a second call to `TRANSLATE` to preserve only the "good" characters.

    DECLARE @WhiteListedCharacters NVARCHAR(1000)
    = ' !"#$%&''()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ'
    + '[\]^_`abcdefghijklmnopqrstuvwxyz{|}~'
    
    SELECT text,
        BadChars,
        Cleaned = REPLACE(
                      TRANSLATE(
                          text  COLLATE Latin1_General_100_BIN2,
                          BadChars,
                          REPLICATE(N'ψ', LEN(BadChars))
                          ),
                  N'ψ', N'')
    FROM sys.messages
    CROSS APPLY
    (
    SELECT REPLACE(
               TRANSLATE(
                   text,
                   @WhiteListedCharacters COLLATE Latin1_General_100_BIN2,
                   REPLICATE(
                       LEFT(@WhiteListedCharacters,1),
                       LEN(@WhiteListedCharacters + '-') - 1)),
                   LEFT(@WhiteListedCharacters,1), 
        	'') AS BadChars
    ) ca
    WHERE language_id = 1038