Insight meditation
 

My favourite type of meditation is insight meditation, or mindfulness meditation, or vipassana. However this seems to be strictly Buddhist and I'm not a Buddhist and feel like a fraud if I go to a meditation sitting.

If you are being mindful in meditation, then you are being mindful and that is it. Say you are concentrating on your breath. That is not Buddhist or non-Buddhist. It is just your breath and your awareness. Buddhism does not hold any copyrights to your breath or to being aware of your breath :-)

It is important also that Buddhism isn't meant to be a cult that you have to submit to in order to access anything it offers. It is only meant to benefit us, help us and free us from suffering. If you don't believe in any particular teaching or doctrine that is ok. Just use the methods offered as much as you find them beneficial.

Well first, you can certainly meditate on your own; you don't have to go to a group meditation to meditate effectively. Also, no spiritual tradition has exclusive rights to any practice, and most are very happy to facilitate learners as well as people who just want to go once in awhile for the experience. And you definitely don't have to be Buddhist to go to those meditation sessions. Buddhism is known for being one of the most open and accepting religions. I wouldn't worry about it if you're interested in going