Politics in general can get emotional. Politics affects people. When people fight for what they believe, they are speaking for many people. How could you not get emotional over that? That is to say that we all get emotional, but a key difference with Democrats is that we're usually fighting for the little guy. It's a lot easier to get emotional about ensuring two people who love each other can wed, despite being the same sex, compared to getting emotional over billionaires getting a tax cut.
Yes, Democrats get emotional. They don't get over-emotional though. The comparison in stereotypes would be that Republicans are heartless. If you're a Republican reading this, reflect on what views you may have that could be described as heartless. I get emotional when talking about my politics because a lot of my focus is on people who are hurting. Sorry, not sorry.