How to read papers without falling into a rabbit hole? Often while reading a paper, I will see a citation that that seems more relevant than my current one. I'll switch to the new paper, only to experience a similar feeling. Or maybe I need to look something up on Wikipedia. An hour later, I'll still feel as if I didn't really digest anything. I will have skimmed 2-4 papers' introductions and conclusions, scratched some notes on the side, and generally feel overwhelmed.

Is this a bad habit? An abnormal feeling? How have others dealt with this to become more productive readers?

I'm fairly new to research, if that matters.
Your problem is quite common among researchers. Actually it's not really a problem, being overwhelmed like this is just natural. Me and all my friends and colleagues face it. 

How I overcame this issue: I try to focus on one paper at a time. Try starting reading the latest research paper on a particular subject and go back chronologically. Print the research paper in hard copy, leave your computer and cell phone (if possible) behind and start reading the paper. The point here is to avoid internet access. No matter what question you have, do not search it right away. Write it on the side notes and keep reading. Most of the time the answer will be in the later sections of the same article. Even if you do not get the answers, once you finish reading the paper, you can go online and find all the answers. That's how I read literature without falling in a rabbit hole. 

Also, reading the Abstract first, then the conclusion, and then the rest of the paper is also effective. 

For me, changing place of study also helps to focus and good instrumental music is always a plus.