This is the kind of question that can easily become a strongly held conviction. But should it?
Well, people do benefit from seeing the text, and seeing it in the same translation as the speaker, and without the hassles, distraction, or potential embarressment of having to look it up in their own Bible, which of course, they may not have.
On the other hand, people who don’t need to bring their Bibles to church, won’t bring their Bibles to church, and won’t develop the ability to look up references, nor to see passages in their contexts – instead getting used to the idea that verses stand alone in picturesque vacuums.
Some will offer a compromise. The main text will not be projected, but the cross-references will be projected so folks can keep their finger on the main preaching text and not get caught up or discouraged in a melee of sword drills throughout the message (which, as a passing comment, I would suggest is not that helpful most of the time, even if folks can keep up).
So what to do? My suggestion is to be a bit situational. What kind of church is it? What kind of service? In an evangelistic service perhaps it is worth it to avoid any embarressment or discomfort, but in a Bible study for believers surely they would benefit from having a finger on the text in its context? What kind of sermon? Perhaps a special event is not conducive to people carrying Bibles.
Some have a tendency to make every matter one of strong conviction. This tends to dilute the effectiveness of such convictions. Don’t allow the deity of Christ, the relationality of our Triune God, the inspired nature and centrality of Scripture, the exclusivity of faith (not faith-plus), the importance of an expository philosophical commitment in preaching, etc. . . . don’t allow important convictions like these to get lost in a sea of passionate commitments to which version of the Bible people should use, or what people should wear to church, or to preach, or whether the south Galatia view trumps the north Galatia view, or whether believers should drink alcohol, or how long a sermon should last, or whether the Bible text should or shouldn’t be projected.
As preachers, even as believers, we have to form opinions about many things. But let’s reserve the passion of convictions for that which really counts. Should Bible texts be projected? Maybe. Sometimes.