Inflation does have distributional effects, and perhaps he's simply looking to protect those who gain most from price stability. That said, the winners and losers from inflation aren't as obvious as one might think. It's not clear why this should be a Republican cause.
Perhaps there's a short-run political gain to playing Chicken Little during a moment in which the extreme elements of his party remain engaged even as most of the public is tuning out politics. But Ryan is an ambitious character, and surely such extremist views will prove to be a liability when the broader public tunes in to the 2016 election campaign.
The remaining possibility is more frightening. Perhaps Ryan really does believe this stuff. Perhaps the chairman of the House Budget Committee is actually an inflation nutter. Even more scary, perhaps he's willing to act on his fears.