So…I have an old single speed road bike (a trek district) and want to fit a 29er alfine wheel. The wheel axel is too wide so I’ve had to pull apart the rear stays to force in the wheel. It seems to work ok but is it dangerous?

Should be OK, you may be able to respace the hub

It’s not uncommon to force the stays apart and many do with out issue. Personaly Id rather narrow the hub

It’s not going to do the frame any harm, but may make your chain noisy as the chainline will shift. Probably nothing really noticeable though..

Is the frame made from Alu or steel?

It’s unlikely you’ll meet the yield point of the material with your hands so it should be ok.

Elastic deformation is ok. Plastic deformation is a no no. Youngs modulus and all that

its an alu frame…will that make a difference?

You’re going from 130mm to 135mm I take it, so 2.5mm a side. Apart from a bit of faffing to get the wheel in it’ll be fine whether steel or aluminum.

Several of my wheel/frame combinations require a bit of force. I’m not sure what spacing they are supposed to be, actually. That includes an aluminium frame with 80,000k on it, so don’t believe the doom-mongers who say they will crack. They aren’t any more prone to it than steel frames, though to be fair the latter are easier to repair (though on second thoughts the number of cracked frames that are worth repairing is pretty small, so it’s not really much of an advantage).