Some Church members, including some who should know better, still occasionally repeat the old Mormon myth that guitars in sacrament meeting are forbidden. Let me set the record straight. According to Handbook 2, Administering the Church ("the red handbook") Section 14.4.3, Special Musical Selections, page 116, "Musical selections may be presented by choirs, vocal and instrumental soloists, and small groups. Hymns and other appropriate selections may be used (see 14.4.2)."
Section 14.4.2, "Guidelines for Choosing Appropriate Music for Church Worship Services," is lengthy, but contains the following citation relating to musical instruments used (emphasis added):
"Music in Church meetings should not draw attention to itself or be for demonstration. This music is for worship, not performance. Organs and pianos, or their electronic equivalents, are the standard instruments used in Church meetings. If other instruments are used, their use should be in keeping with the spirit of the meeting. Instruments with a prominent or less worshipful sound, such as most brass and percussion, are not appropriate for sacrament meeting."
These two citations are the only ones relating to permitted instruments in the entire handbook. Not a word about guitars, though I suspect that electric guitars, with heavy distortion, would probably be disqualified as having "a prominent or less worshipful sound."
I have played my classical guitar in sacrament meeting many times, as well as in two different Missionary Training Centers, including the Provo MTC. No one has ever claimed that my music was inappropriate, after hearing it. If anyone challenges the appropriateness of your playing a guitar in church, challenge them to back up their assertion with a quotation from the official Church leadership handbook. It is available online through lds.org.