Is it acceptable to e-mail a professor at another university to ask for a meeting to discuss common research interests? I'm a PhD student, from Europe, nearing the end of my thesis. 
I'm going to the USA for a conference in a few months. A couple of professors (assistant professor level, both fairly young, recruited in the past 2 or 3 years) whose work I'm very interested in teach in the vicinity of the conference venue.

Would it be acceptable for me to e-mail them out of the blue and ask them if they'd like to meet/have coffee to discuss common research interests? 

They both do literature like me and care about similar methodological issues. However we work on (and in) very different geographical areas, so the chance of us ever meeting at a regular conference are low. 

Is this ever acceptable? Does rank/school factor into it?
The answer is simple: yes, it is acceptable and common. Don't worry about your rank or about the status of your school. If your email is polite, friendly, is not too long but still includes enough relevant information about you to make it clear to the professors that you and they have shared interests, I estimate that the chances of success (meaning they will agree to meet) are very high — basically the only reasons why this may not work are if the professor is out of town on the day you are proposing to visit, is overwhelmingly busy with other commitments, or is an unpleasant and unfriendly person you probably wouldn't want to meet anyway. Good luck!