When playing online, you might see other players touching moving traps or getting hit by projectiles, but they survive as if nothing happened.

That is due to how the game is networked - it does not mean players are cheating. 

In Ultimate Chicken Horse, when you're playing online, the location of all blocks and projectiles is calculated and displayed locally for each player. This means that you can always know precisely where platforms and traps are, and you can play without a lag disadvantage, just as if you were playing locally.

When playing online in Ultimate Chicken Horse, the locations of all blocks and projectiles are calculated and displayed locally for each player. This means that you can always know precisely where platforms and traps are, and you can play without a lag disadvantage, just as if you were playing locally. 

However, there will often be desync in the block animations between you and other online players, so that each player sees them in slightly different places. When the position of each other player is shown to you, it might look like they're standing on air, or being hit by projectiles without dying, but that's not what it looks like to them.