Conservatism is an ideology(often associated with right wing ideologies) that believes that the current way, or a former way is a better one. There is no reason why it doesn't belong in a democratic society.
But there are conservative streams that are less democratic. Religious conservatives for example sometimes oppose women's voting rights, which of course damages their democratic rights.
But depending on what nation you live in a Conservative party can have a great difference in meaning, even within the borders of a single country there can be conservative parties that, based on religious ideologies, have highly different views.
For example, the Netherlands has several conservative parties, Two of them are the PVV and SGP. Both are Dutch conservative parties, but the PVV is not religious based while the SGP is Christian based. One huge difference between their ideologies is that the PVV supports gay rights, because they believe that equality towards gay people is a fundamental part of Dutch society. the SGP on the other hand opposes gay rights due to their religious nature.
The reason why Conservatism is placed in a bad daylight is because they oppose change in the forms of immigration. Conservative parties want their nation to stay as it is on fronts like culture, this often gives them anti immigration leanings or anti religious leanings towards religions that are not common in their homeland.
Most of the Islamic dominated countries have conservative parties who want to hold to it, and often oppose foreign/minor religions like Judaism. Just like several western conservative parties oppose Islam. Another point is language and ethics.
I myself am a Dutch conservative and personally find it ridiculous that some of our districts have voting ballots that are not in Dutch, to help immigrants who don't speak Dutch to vote. Also I think that women's rights trump religious rights, and that our culture should be preserved on that front. (for example a while ago on a local level we had issues that immigrants refused to accept help from female social workers because it was not their place to offer help to men).