If you're using PCRE, you can use a control verb to skip everything inside of a quote closure:
(['"`]).*?\1(*SKIP)(*F)|\\n
(['"`]) any type of quote, put it in group 1
.*? any characters, non greedy
\1 the quote that captured in group 1
(*SKIP)(*F) skip the current match, which is a quote closure
|\\n match a \n
See the test cases
Also, if you need to ignore escaped quotes(\"
, \'
etc), you may try
(['"`])(?:(?<!\\)\\(?:\\\\)*\1|(?!\1).)*\1(*SKIP)(*F)|\\n
Check the test cases
Using JavaScript
For JavaScript, you can't use control verbs. But you can use group capture to replace outbound \n
((['"`])[\s\S]*?\2)|\\n
$1
const regex = /((['"`])[\s\S]*?\2)|\\n/g;
const text = String.raw`\nnew"test\naaaa"\nta\n\`this is a \nnewline that should be kept\`\ntest\n'this \n should also be kept'\n`;
console.log('before\n', text);
const result = text.replace(regex, '$1');
console.log('after\n', result);
const regex = /((['"`])[\s\S]*?\2)|\n/g;
const text = `\nnew"test\naaaa"\nta\n\`this is a \nnewline that should be kept\`\ntest\n'this \n should also be kept'\n`;
console.log('before\n----\n', text);
const result = text.replace(regex, '$1');
console.log('after\n----\n', result);