What is likely true is that first/given-name form of address expresses a peer-relationship attitude. In some contexts, there is a nearly-mandatory pose that "we are all peers", etc. While, ideally, this is true at a moral or civil level, it is equally obviously false in terms of sheer experience, and, usually commensurately, expertise.
(There is an auxiliary-but-related question simply about age... Given the extreme disparity between my own kids and myself, I don't expect them to address me by my first name... nor as "Professor Garrett" ... but hopefully by some affectionate honorific that does acknowledge (the complexity of) our relationship. Similarly, I pointedly adopt a stylized form of address for my kids. We are all acquainted with the trope that when the mom addresses the kid by the kid's full name, they're in trouble. I myself, especially at the point that I'm older than many postdocs' parents, have a similar feeling about that relationship. Opinions differ, of course.)
Use of an honorific, even if informal-honorific, form of address does express respect. Use of given name expresses familiarity, etc. At worst, given-name address implies a sort of "good ol' buddy" relationship that verges on the demeaning.
Perhaps the genuine issue isn't the words uttered, per se, but the tone-of-voice and body language. But, if we agree with this, then the original question becomes enlarged to the question of whether one should express deference or respect for ... ok, the real question is about how one fills in the blank about the object of this sentence! If it's "one's boss", well, one does what is necessary. If it's "one's mentor/teacher", then perhaps a systematic tone of respect is appropriate. If it's simply "the old person", then who knows? What is your attitude toward your mentor/advisor/teacher?
Operationally, as in some of the other answers, unless there's a pervasive conformity pressure to do "given name address", surely it's better to err on the side of slightly-excessive expression-of-respect, rather than the other way. Wait till some says "Please, just call me ...", rather than the awkward opposite.
(In French and some other languages perhaps-inappropriate first-name address used to have its own name: "tutoyer", meaning to address toooo many people with the familiar "tu", rather than formal-er "vous", but I gather that times have changed...)
In terms of quips, I might suggest that, ... in contrast to the suggestion that if your thesis advisor or postdoc mentor doesn't want you to call them by their first name,then get another, ... if you don't have a mentor you respect enough ... for good reason, that their expertise and insights are nearly-unimaginably superior to yours at this point in your career... to throw a little honorific their way, then you should get a new advisor/mentor.
People won't be offended by your being too polite and respectful, but may be by the opposite. Pretty straightforward, I think.