You can see in the aboutCV page of Stackoverflow Careers site that the word resumes is mentioned — not résumés or résumés.
What should be the common practice here?
What about other words like café?
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The diacritics no longer serve their purpose in most cases of providing phonetic information and it can be said that they are largely being obsoleted. There are cases where their use is important though, e.g., as a form of social signaling, just as knowing the etymological origin of English words, especially from Latin and Greek marked a person as educated.
For example, résumé is word that you will often see.. Knowing these diacritics (and probably the origin and the raison d'être) highlights you as knowledgeable, especially to a potential employer. In another case, you would never scribble a note to your neighbor to take care of the fish because you booked a night at your favorite hôtel. Certain words have retained them, while many others haven't. I would say the choice to use them comes to a choice of register in a social context.
It's rare these days to see diacritics in words that were borrowed a long time ago and have become essentially "nativized". That certainly includes resume and cafe. You do occasionally see them used, especially in older writing or in cases where an air of foreignness is desired.
I would say that it's ok to use them, but you should be aware that it will stand out somewhat to most readers and is not really standard anymore.
Diacritics are still essential as missing them out often implies an anglicised pronunciation. The problem is that most people don't know how to type a diacritic mark on a standard keyboard. Useful pointer is that ALT + 130 gives the most common diacritic mark é.
The loss of diacritic marks often results in mispronunciation. For instance a coupé is a sports car and is pronounced coopay. A coupe (pronounced coop) is a bowl or champagne glass.
Résumé is a CV or summary of your work experience. resume is to restart.
Café is pronounced cafay, cafe would rhyme with safe.
Zoë, Noël, naïve would be pronounced Zo, Nool and knave without the diareses.
Façade is pronounced fass-ahd, facade would be fack-ade.
Olé is pronounced olay, ole rhymes with hole (or IS a hole in London as in "he dug an 'ole").
So to answer the question, YES the accents in loanwords should still be written with the accents as not doing so will result in mispronunciation or ambiguity.