What does "Küssen bei Sympathie" mean? The English translation doesn't make sense.
Sympathie affection, fondness; goodwill
You sentence seems to come from the context of sex workers offering services in advertisements. There, küssen bei Sympathie means that the prostitute is willing to kiss you if (s)he feels comfortable with you and/or likes you and/or you appear well-groomed and "clean".
Here is a Spiegel article that uses the phrase in the title of an article on prostitution during the "Corona crisis": "Küssen bei Sympathie": Warum Prostituierte trotz Corona arbeiten – und wie
Other Google finds lead to punter forums and ads by prostitutes that I don't want to link here. You can easily find them yourself.
Both Sympathie and sympathy come from the greek word συμπάθεια, meaning having an emotionally positive stance for someone, or showing them love (preference if you will).
Just like in Greek, Sympathie in German means affection and love for someone. A synonym for that in German would be
die Zuneigung (Sg.).
The fact that the English translate to sorrow for someone's misfortune, is because through the translation the actual meaning has been altered.