Yes, it is. It's an all too common misconception that this could cause problems with your engine, and one with no scientific data to support it. When switching from a mineral oil to a synthetic, or vice versa, you will potentially leave a small amount of residual oil in the engine. That's perfectly okay because synthetic oil and mineral-based oil are compatible wtih each other, that's why there are synthetic blends on the market. In fact, most oil changes performed at quality facilities, now incorporate a synthetic/mineral oil blend because of it's proven long term protection and added value.
There was a time, years ago, when switching between synthetic oils and mineral oils was not recommended if you had used one product or the other for a long period of time. Some operators experienced problems with seal leakage and high oil consumption but changes in additive chemistry and seal material have taken care of those issues.
Why change oils from mineral to synthetic? The biggest benefit of changing to synthetic or a semi-synthetic motor oil blend is it's ability to maintain it's level of performance at extreme temperatures, both hot and cold. It's especially important in vehicles that have a turbo, to use a full synthetic oil. Because of the high heat produced by the turbo, mineral-based oils can "cook", thicken up and turn to sludge, while a full synthetic oil retains it's viscosity. The same is true in the extreme cold. A mineral-based oil tends to thicken up in the cold, while synthetic oil does not. Additionally, if you use a full synthetic oil, you can usually spread your oil changes out a bit beyond the standard 3000 mile intervals. Ask your service advisor for details on your specific vehicle requirements and driving conditions.
What about those $19.95 oil changes? As the old saying goes, "You get what you pay for". These usually include the cheapest oil, filters & labor available.