It means a suggestion of. So in this context it means that some people may think it carries disapproval by themselves are others

An overtone is an implicit message which is perceived as overwhelming an explicit message. So even though fornication is consentual sex between two unmarried people (the explicit message), others/most people are still going to think you are slutty and/or nasty (the implicit message) due to the moral and religious values they have. :) An undertone is more of a subtle suggestion. That is, people wouldn't care if you had sex without being married but they would also recognize that it is considered nasty in the eyes of the church on some level. :)

It means the same thing as 'connotation' or 'association'. That is, it carries meaning(s) beyond or in addition to the explicit definition of the word.