IMO, Islam itself isn't a threat to democracy. It is the people who misinterpret the Quran to spread violence (example, muslim extremists) are the ones that are a threat.
For example, many people list quotes from the quran such as:
"Qur'an (2:191-193) - "And slay them wherever ye find them, and drive them out of the places whence they drove you out, for persecution [of Muslims] is worse than slaughter [of non-believers]...and fight them until persecution is no more, and religion is for Allah."
This quote is about self defence, not attacking. The quran does not promote violence unless it is in self defence. Although people misinterpret it to say it spreads violence. In the Quran, the muslims were actually driven out of their homes by the pagans and the muslims wanted to protect their homes and hence this is self defence.
For example, if the above quote spreads attacking violence then you could say that Winston Churchill's quote:
"we shall fight on the seas and oceans,
we shall fight with growing confidence and growing strength in the air, we shall defend our Island, whatever the cost may be,
we shall fight on the beaches,
we shall fight on the landing grounds,
we shall fight in the fields and in the streets,
we shall fight in the hills;
we shall never surrender"
Spreads violence, however, Winston Churchill said that quote as SELF DEFENCE not attacking.