"Can you really experience anything objectively without emotions?"
I see no one knows what the word objective means. Why this keeps happening, I don't know but it is a bit idiotic. Objective would seem to be a pretty easy concept to grasp.
Objective: "(Of a person or their judgment) not influenced by personal feelings or opinions in considering and representing facts."
For example: You are reading my post right now. You are recognizing my words as English and understanding their individual meaning. This is objective. You are seeing and understanding the same thing I am seeing and understanding when I read this. You don't need your feelings to understand what this post means.
Objectivity does not entail your experiences, which are subjective. It entails your external reality. And despite the fact that we rely on our brains to interpret that external reality on an individual basis, that reality does exist independent of our minds, and we are capable to understanding that reality in ways that are recognizable across individual experience. Get hit by a car going 100 Km per hour and regardless of your subjective experience during the event, you are still objectively injured. This will be the same for any individual getting hit by a car going 100 Km per hour, barring an statistical anomalies.
The only way in which we would never experience objective phenomena is if all reality is dependent solely on our minds and no external agents. In other words, the mind creates reality. But as modern science has proven, this notion is extremely flawed, falsifiable, and verifiably wrong. Objective phenomena is defined as reality which exists independent of our own perspectives. This means that even without a conscious observer, the phenomena remains real. The moon remains in the night sky despite whether or not we are looking at it. Gravity would continue to work regardless of if we were standing on the earth. A wall is still solid regardless of whether or not you are touching it.
Some people may want to believe that they go through life creating their own reality and never encountering a single fact. My opinion of such people is that it's primitive thinking and that they are obviously suffering under a strong delusion and need therapy.