If inflation and returns on saved money are consistent then it will have little impact on savings rate. But, in general it is a good idea to try to stabilize the value of the currency, although demand pull inflation needs to be separated from commodity shock inflation since their causes and the actions taken to mitigate are likely different. Demand pull inflation as a result of there being more financial assets (currency) chasing a relatively fixed amount of real goods is mitigated by draining currency via narrowing the deficit of the currency issuing government by raising taxes and/or decreasing spending. And, the reverse when deflation threatens due to recession.
Some of this is automatic, and already exists. On the revenue side, income tax receipts increase as more people have jobs and income tax receipts increase, if incomes increase enough, a progressive income tax causes the deficit to narrow even more. On the spending side, unemployment insurance, food stamps, and other safety net spending will tend to decrease, narrowing the deficit further. In an economic down turn when deflation threatens these act in the opposite direction. I would prefer additional more powerful automatic stabilizers, but these are a few examples of controls on demand pull inflation/deflation.
I don't know enough on the commodity side to say how that should be handled, but hoarding of useful commodities via ETFs backed by actual warehoused commodities held off the market should be banned.