1 Correct answer
The automatic Curly Quotes option is a one-time Special Offer only, and as soon as they are inserted in your text, curly or not, they're going to stay that way.
... It is rather tempting to promote my own IndyFont here. ("Create a font where the curly quotes lok like straight ones and apply it through a GREP style in your 'code' paragraph style, done.") But I won't because I am a code purist 
and it's not a problem to change the quotes to their proper form.
You can safely use Find/Change to change
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Replies
You can insert them directly from Type > Insert Special Character > Quotation Marks > Straight [Double/Single] Quotation Mark(s)
Or you can use the keyboard shortcuts.
You can select and then load them into Find or Change and Find / Change in your selected code for quotes that already exist.
There may be other ideas.
The automatic Curly Quotes option is a one-time Special Offer only, and as soon as they are inserted in your text, curly or not, they're going to stay that way.
... It is rather tempting to promote my own IndyFont here. ("Create a font where the curly quotes lok like straight ones and apply it through a GREP style in your 'code' paragraph style, done.") But I won't because I am a code purist 
and it's not a problem to change the quotes to their proper form.
You can safely use Find/Change to change all curly quotes in code to straight ones. With a plain text search, search in turn for ' and " and replace with ^' and ^". Make sure to specifiy your "code" style in the Find Format. This will work because by default, when looking for ' InDesign finds all kinds of single quotes, curly or otherwise. The replacement string ^' in turn forces a straight quote, regardless of the setting of your Typo Quotes in Preferences.
(By the way, did you take care to switching ligatures off for your code snippets?)
Here is how it would work.
1. Create a new font where the curly quotes appear as straight ones in the code font in use.
2. Apply the custom font to just curly quotes using a GREP style.
3. Done. I added a yellow background in the character style so you can see where a curly quote is changed to look like a straight one.
IndyFont is for sale at IndiScripts: Indiscripts :: IndyFont
You can try this with the free demo, but beware that it only allows you to create one character per unique font. (You can still do what I did here, but you'll have to create a unique font for each of the curly characters.)
That said: I would not advocate this approach. Suppose someone copies the code out of a PDF; then, the curly quotes would return, and that code would not work! The same goes for exporting to a HTML page or an ePub. You can compare it to making a text correction by pasting new text in a white box over the wrong word – it works, kinda, in a PDF, but nowhere else.
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