How do I keep my rockets from blowing up the pad without launch stabilizers?

Solution 1:

If this is happening for smaller rockets then I suspect this is a loading glitch.

When a rocket is "moved" to the pad, it literally spontaneously appears there (what else would it do?) while the screen is black, then physics is applied too it. This would be fine, however the simulation is also building up textures and loading up all sorts of data at the same time.

If the rocket gets physics applied to it before the collision mesh for the Launch pad, the rocket will spend a few critical milliseconds falling through the pad. This will either result in the destruction of the rocket or the destruction of the pad.

There are only two solutions to this:

  1. Launch Stability Enhancers. (They keep the rocket from falling)
  2. There is a mod call Kerbal Joint Reinforcement, one of the many things it does too enhance the stability of rockets is to stop physics from being applied immediately, instead dialling it up over time

Solution 2:

Make your rocket wider, so there's less mass per surface area.
Also makes your rocket more stable, less likely to topple. Of course it can become unstable if it's not properly strutted...

And play the game as it's meant to. If you don't have the launch stabilisers, just make rockets that don't need them to remain stable. You can easily make a rocket that takes you to the Mun or Minmus that's small enough to not need them for example.
Haven't tried rockets going further than that, but I guess Duna should be possible, certainly a one way mission.