I'm particularly curious as to what kept the soldiers of the HRE from joining with the peasants- it seems to me that most of them were peasants themselves, so why wouldn't they be sympathetic to the cause?
Is it likely that they'll win? Noting that soldiers on the losing side tend to get massacred.
Class solidarity is not a particularly important concept at the time. Religion, the established order, and personal loyalty are more likely to inspire a soldier than a (to him) abstract concept of class. The rebels are causing upheaval, they are going against the divinely-ordained order of things, and they're fighting my prince. (Who is also my paymaster, for those not inclined to personal loyalty.)
The soldier may not even know what the peasants' grievances are - can he read? Do the peasants hand out pamphlets? Even if he does, they're not his grievances. That stuff happened to some other set of peasants. Again, class solidarity is just not that important at the time.
The peasants are burning productive assets and destroying infrastructure wherever they go. Those pigs and sheep they steal - "requisition", if you like - were going to keep someone alive through the winter.