Is pushing people considered a hostile action? Do you need a DM to do it where NPCs are around? How can one react to the "push" clearly someone in full plate won't be pushed as easy compared to someone in leathers. I know strength rolls are what would come to mind, but there is no DM to enforce the rolls.

A reasonable reaction to being pushed is to push back at the very least. It is a hostile action, and if in front of NPCs it is required you do get a DM and set your target to hostile beforehand. This will avoid a heap of trouble.

As for the difference in platemail/leathers, it is by and large negligible.

If someone says *pushes x* you can emote whatever, *doesn't fall over* or whatever.

There is no mechanical representation of pushing.

And to expand on what Caddies said, if you're pushing as a means of instigating a fight or harassing someone, get a DM.

If you're just shoving past a crowd or whatever then it doesn't matter.

Oh, yes. Pushing past someone is fine!

I thought you meant in the context of an argument, or to incite violence.