It's an interesting question. My gut feeling is that everyone should be involved in politics.
We're all part of society, so it makes sense that we should all be interested in how it's run and to make sure our voice is heard and represented.
The only negative I can see from students getting involved in politics is that it can be easy to get carried away and influenced by peer pressure or propaganda when you are young and don't have the "experience" to handle all the media spin and falsities we are subjected to these days in the form of politics.
Also, when tempers flare around student political activity, people sometimes caught up in violent clashes and even police brutality... Which I don't think anyone wants to get involved in!
This is especially likely in countries where public protesting isn't allowed.
