I think most people know that cell phone signals can interfere with airliner avionics; that's why airplane mode exists. Is this an issue with small GA planes?
You are mistaken. Cell phones are not banned onboard because they do interfere with airliner avionics. They are banned for two reasons:
because their use while airborne interferes with ground-based communications. This is an FCC rule, not an FAA rule, and has nothing to do with the aircraft and everything to do with the consequences on the ground. See FAA AC 91.21-1D, at 9.1 "Restricting Airborne Cellular Telephone Use," and 47 CFR §22.925.
because it is possible that certain portable electronic devices could interfere with aircraft navigation or communication systems. The FAA permits the operator of the aircraft to allow any portable electronic devices once they have determine that they in fact do not interfere with these systems. This is in CFR 14 §91.21 for Part 91 operations, and there are similar rules in Part 121, 125, and 135 operations. This same rule applies to most electronics- even in airplane mode and even if they do not intentionally transmit radio waves, the default rule is that they are not allowed. In practice, many operators allow them during at least some phases of the flight.
In short: any portable electronic device has the "potential" for interfering with aircraft systems. It appears that most of them, at least most of the time, do not do so significantly. Occasional reports of possible PED interference have proven rare and difficult to replicate. See for example this and appendix I in this document.
Regardless of any interference with aircraft systems, cell phones in particular are forbidden by the FCC any time you are airborne.