:salam2:
There is no problem with democracy in Islam. Actually Islam introduced democracy to the world. The process is a little different but the concept is the same. People nominate a person and other people approve them by putting their hands on the hand of that person (called bayah), or reject them.
This is how the Khulfa-e-Rashedeen meaning the first 4 Khalifas (rulers) were elected.
At that time Khaifas were elected for life, but with a catch... If it is found that they have done anything sinful or against Islam hudood laws then they could be removed from that position.
But these processes were not cast in stone or prescribed in Quran. So a process of putting name on a paper or selecting name in a paper (ballot) instead of putting hand is perfectly right.
And these days there is voting happening everywhere. In many Muslim countries this process is used of people giving vote to elect their representative or leader. You can call it democracy or whatever.
So there is no issues here. I know, Some people are too picky and I don't want to comment on this kind of attitude. Some people just don't like the word democracy... go figure.
I just ignore them.