I just started a job 2 months ago, and realized I absolutely hate it - extremely political and the boss is unreasonable. Should I state my current experience if I apply for another job now?

I will recommend you a book which was invaluable to me in my career.

https://www.amazon.com/Career-Warfare-Building-...

This is perhaps the best career book I have ever read. Coming from someone who won the ladder. His advice spans in situations like yours and in others. Having this is like having a CEO as your adviser in your corner.

TLDR: There are times when you are in a situation like this and the only way for you to manage this is simple: Manage your boss. We have good bosses, we have bad bosses. Changing jobs doesn't help you much if you aren't learning from it. Take this opportunity to learn from this experience to bring with you to the next job.

Yes, why not? You will burn your youngth faster when you work for a company like that. If you extremely hate it and want to leave, state whatever you think you should say. If they have a negative mind, they don't want to change and that's good for you to leave. If they take your feedback in mind and change, they will see you as a valuable employee and keep you.

If they fire you, you can also tell that story in the next interview if the interviewer asks you why you leave your previous job. It may be an advantage competitive for you during the interview. Just be honest with the interviewer, tell them the true story, you can build your trust easily. You can visit these job portals TalentTribe, Jobscentral, LinkedIn, Mycareersfuture and Jobstreet for your next job search :)