MT and kyokushin karate works pretty well together, and they combine just fine.
The formal karate training is very different from what you do in MT, but once you start sparring, or break out the bags&pads, the differences is mostly just rules&equipment (no head-punches or clinch vs gloves & no sweeps). The techniques and attitude is very similar. MT has better elbows&punches against the head, and a better clinch.
Kyokushin has better body-punches, better bareknuckle skill, sweeps, and a greater variety of kicks.
Having said that, training two styles at the same time usually means slower progress in each.
If you are not already accomplished in MT stick with it for a while longer before you start to crosstrain.
When you do, check with the instructor of the kyokushin gym. If you are polite about it, there is a chance he may allow you to get into the heavy duty fighting with the advanced guys quicker, rather than have you dominate your fellow newbie whitebelts.