Most established definitions of democracy goes something like, heavily simplified:
1. Free media
2. Independent judicial system
3. Peaceful system for the transfer of power
The most popular model for implementing (3) is free and open elections, which has yielded pretty good results in the past century where it has been practiced.
Considering social media pretty much is media for most, it is a heavily concentrated power, and if there can any suspicions of being in cahoots with established political power and thus non-free, surely that is a threat to democracy almost by definition.
Let's be real here: It has been conclusively shown again and again that social media does influence elections. That much should be obvious without too much in the way of academic rigor.