But, if you are unsure and looking for my opinion, I would say it's usually better to push with your back foot. If you are just learning to skate, this is a good time to re-learn to push with your back foot. Pushing "mongo" can get in your way, with you having to shuffle your feet around before doing technical tricks.
If, however, you have been pushing mongo for a long time, it can be a little more tricky to decide if you should switch or not. There's nothing wrong with pushing with your front foot. At all. The only problem is that most skaters push with their back foot, and a lot of people agree that this is the better way. But, if you've already pushed with your front foot for a long time, and it's not getting in your way, then why not stick with it?
Another thing to consider, unfortunately, is that if you are a young new skater and push mongo, other skaters might make fun of you for it. Which is lame, and no reason to change how you skate. In fact, if that were me I would be tempted to keep pushing mongo just to rub it in their faces. But, not every skater is as aggressive as I like to be in my imagination... On a total side note, if you are in this position, you really need to get over caring what other punks think of you. It will hold you back until you do.
So, the answer to the question we started with - "is it OK to push mongo?", is yes. You can push mongo all you want. But, my advice is to push with your back foot. I think you'll be more stable, and be more quickly set up to do tricks. But, if you already push with your front foot and it's working for you, then why change?