I palindrome the source code, you palindrome the input!
Haskell, Full program, 39 bytes
iddi=(++)&lt;*&gt;reverse;main=interact--
 id

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Mirrored

iddi=(++)&lt;*&gt;reverse;main=interact--
 iddi 
--tcaretni=niam;esrever&gt;*&lt;)++(=iddi

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Very simple approach for a full program.  We have two &quot;lines&quot; (separated by ; rather than an actual line break) of boilerplate ending in -- and then the function id.  When the program is reversed id gets changed to iddi, which we have defined to do the intended operation.
Haskell, Function, 20 bytes
f x=x--x esrever++ 


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Mirrored
f x=x--x esrever++ 

 ++reverse x--x=x f

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This one is also a pretty simple approach.  We have a function f x=x and   a payload hidden in a comment.  When the code is revealed the payload extends our function with ++reverse x.
Haskell, Function, No Comments, 95 bytes

i=id
ko 'a' b=i id b
ko u m=i reverse m
u=flip ko
k s=&quot;ab&quot;&gt;&gt;=s
yf i=k&lt;$&gt;u
erehw l=l
fy=i erehw 

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Mirrored
i=id
ko 'a' b=i id b
ko u m=i reverse m
u=flip ko
k s=&quot;ab&quot;&gt;&gt;=s
yf i=k&lt;$&gt;u
erehw l=l
fy=i erehw  where i=yf
l=l where
u&gt;$&lt;k=i fy
s=&gt;&gt;&quot;ba&quot;=s k
ok pilf=u
m esrever i=m u ok
b di i=b 'a' ok
di=i

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The relevant function is fy. This one is likely not optimal.  I will explain it when I shorten it down a bit.