"Everyone has their own likes and dislikes about A" would be used and accepted in everyday English. I would not use the singular "their" in careful or formal English. " (or phrase it another way altogether to avoid the issue).
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teacherJapanIs it relatively common to use the phrase 'Everyone has their own likes and dislikes about A' to mean 'A varies from person to person'?No. Not at all. Consider:
GPYI assumed in my reply that the question really intended to ask thisYes, that makes more sense. In a previous life I was trained as a mathematician, so I treat variable substitutions literally. Occupational hazard.