I don’t have any hard facts on when this tack became plausible or on how pervasive it is (no doubt the bifurcation of Jesus and Paul is somehow a factor), but it seems lately that the claim that Jesus himself did not overtly express concern about a particular spiritual or ethical issue in the Gospels constitutes an argument to the effect that Christian believers need not concern themselves with that issue. This can be (and has been) used in the case of homosexuality, for example: Jesus apparently did not feel the need to address the matter; therefore (so the logic runs), Christian believers are not obliged to take a hard line on whether such conduct is sinful.
Whether the issue at hand is homosexuality or something else, there are at least two significant problems with this approach to dealing with hot-button spiritual and ethical quandaries in our day. First, it proceeds on a warping of the analogy of Scripture, or the commitment to allowing clearer passages of Scripture to help in interpreting more difficult ones. The analogy of Scripture is useful when one text genuinely boggles the mind of even the most careful reader and other relevant texts can be invoked to establish parameters within which the difficult text should be understood. However, in the case of things like homosexuality, the importance of well-ordered doctrinal formulation, the importance of church polity (all things about which, allegedly, Jesus was not terribly concerned), there are texts that come at these topics in a reasonably straightforward fashion (Rom. 1:26-27; 1 Cor. 6:9; 1 Tim. 6:3; 2 Tim. 4:3 ; Titus 1:9; 2:1; Jude 3; Acts 14:23; 1 Tim. 3:1-13; Heb. 13:17; Jas. 5:14; 1 Pet. 5:1-5). Moreover, instead of employing particularly lucid texts in those cases to help in wrestling with difficult passages, the ‘Jesus said nothing about…’ argument actually attempts to use mere silence as the lens through which to view passages concerning homosexuality, etc. In other words, a move with some resemblance to the use of the analogia Scripturae actually lacks both of the conditions for using the analogy: unclear texts and clearer ones that shed light on those that are unclear.