Ok, I'm a biochemist so I have some knowledge here.
I think you'll find that mutation is a key component of the evolutionary process. Mutations occur with each new generation through gamete meiosis. Toxic mutations result in non-viable offspring, disadvantageous mutations decrease the sexual competitiveness of the progeny and advantageous mutations lead to successful mating and perpetuation of the improvement. String enough beneficial mutations together over time and the process known as evolution occurs.
There is of course religious opposition to the overall idea of evolution, as it directly contradicts a number of religious texts (Bible, Koran, etc), which is fine, people are entitled to their beliefs.
However there is no dispute within the scientific world about how the mechanism of evolution works, and there are certainly no competing theories. The evidence in support of the evolutionary process is overwhelming, and there is zero evidence which contradicts it. Much press is made of apparent "disputes" in the biological world, however the evolutionary disputes that do exist are about very fine points of distinction (eg. did "Protein A evolve before Protein B?") and certainly not the overall process.
