Everyone has an accent, usually formed by the first language they learned.
Whether it sounds (to others) like an accent depends on how far the speaker has moved from their childhood home.
Whether an accent is enjoyable depends on how easy it is to understand the speaker.
A thick accent can be almost impossible to understand and some people will give up trying and walk away.
A moderate accent can still be quite stressful because of the effort it requires; many people will tire quickly and try to avoid te speaker.
A mild accent is no problem and the person will integrate well into the society and quickly make friends.
Some of the reactions may be based on cultural prejudices.