Inflation isn't the *consequence* of a tax, it *is* a tax. It's a tax on savings. Regardless of where the inflation money enters the system, it's never in the $100 bill under your mattress.
All fractional reserve banking creates inflation, *by definition*. If the interest rate offered by the fractionally-reserving banks is higher than the natural interest rate (usually around 10%), then people won't take out any inflation-generating loans (since it would be a bad deal compared to borrowing 'real' money). Any interest rate below that generates inflation, and the inflation enters the economy through whatever is bought with the money from those loans. Whatever those things are will experience an artificial, government-created upward pressure on prices since more money is chasing the same amount of stuff. The ***only*** way to stop inflation caused by fractional reserve loans is to place their interest rates above the natural interest rate (usually around 10%). And that's the "Federal Funds Rate", not the rate consumers would get; consumer mortgages based on those loans would be several points higher.
There's no such thing as "supply side" or "demand side" economics. It's all one integrated whole. Those theories are what happens when single-step thinkers, often career academics or politicians, only look at one side of the equation, usually due to a deficit of critical reasoning ability. Same with "trickle up" and "trickle down". It all goes in a big circle.