Anyone who thinks strength doesn't make a difference needs to train with stronger people.
At equal skill levels, the stronger person will win. That's just physics.
With that said, some of the most intimidating people I know in aikido are small women. They make up for their diminutive size with tremendous skill and enormous spirit. Small women absolutely can develop excellent aikido.
But so can men. Which is why competitions are and should be segregated. Judo has weight classes, too, for the same reason.
I am trying to come up with a situation where strenght does make a difference, but for now I cannot think of one.
At equal skill levels the stronger person will win? Really? It is an argument that I have heard men use before. But I do not think that this is true in sports competition or in nature for that matter. It certainly is not true in war or in a fight. And it is most certainly not true in Aikido or in Budo in general.
Over the past decades I have come across many women who where better skilled in Aikido then the men that they trained with on a daily basis. Perhaps because as science tells us, women have better developed coordination skills, while men (especially young men) trust their muscle power to get the job done. In Aikido that trust in muscle power will bring a limit with it in progression.
Having said that; Aikido is not about winning or about competition. It is more about personal growth and that is something that cannot be measured or compared with someone else. Aikido is really a path equally suited for both men and women.
It just hit me; dead weight lifting contests, that is were strength could make the difference!