Welcome to the fray!
Do Scientists, especially who I refer to as "evangelical atheistic naturalists" such as Dawkins, Dennett et.al. apply a different "standard of proof" for naturalist scientific theories than for Design theories?
No. Theories only become theories in science when they have withstood many tests (beginning as hypotheses) and when they successfully explain all of the relevant data. A theory must also be able to make predictions which can be verified.
For example when secular naturalist scientists refer to natural selection in evolution it is accepted as fact that there is such an entity. However can anyone prove the existence of natural selection?
First, there is no such thing as "proof" in science. Theories are never proven. When a theory adequately explains all of the relevant data we can speak of that theory as being supported, but never proved.
Does it have a physical existence that can be proven, or is it the name that scientists hope is the modus operandi of evolution?
You might be better off looking at natural selection as an explanation for a lot of data. It does successfully explain the data, but it is still a theory and has no physical existence nor any need for proof.
It is argued that a supernatural being can never be proven, therefore intelligent design can never be proven. I can say the same for "natural selection", it can never be proven, only accepted on a belief, ie faith, therefore it is not a valid theory.
Natural selection is not accepted on faith, but because it adequately explains the evidence. And it does so better than any other explanation. That is the hallmark of a scientific theory.
So far there has been no scientific evidence provided for supernatural beings. Without evidence of some kind there can be no theories, at least not as the term is used in science. But you are right, many people accept the existence of the supernatural as an article of faith.
What if, as I believe, evolution is the continuous creation by a supernatural being, who created and continues to creathe and evolve the natural world?
How can sceintists accept a belief in natural selection as superior to my belief in the supernatural's continuous creation as the cause of evolution. Where is the proof?
No proof, only evidence. And there is a lot of evidence to support the theory of natural selection.
Unfortunately for your argument there is no evidence for the supernatural, let alone for any specific actions on the part of such beings.
Here are a couple of definitions that might help:
Theory: a well-substantiated explanation of some aspect of the natural world; an organized system of accepted knowledge that applies in a variety of circumstances to explain a specific set of phenomena; theories can incorporate facts and laws and tested hypotheses. Theories do not grow up to be laws. Theories explain laws.
Theory: A scientifically testable general principle or body of principles offered to explain observed phenomena. In scientific usage, a theory is distinct from a hypothesis (or conjecture) that is proposed to explain previously observed phenomena. For a hypothesis to rise to the level of theory, it must predict the existence of new phenomena that are subsequently observed. A theory can be overturned if new phenomena are observed that directly contradict the theory. [Source]
When a scientific theory has a long history of being supported by verifiable evidence, it is appropriate to speak about "acceptance" of (not "belief" in) the theory; or we can say that we have "confidence" (not "faith") in the theory. It is the dependence on verifiable data and the capability of testing that distinguish scientific theories from matters of faith.
Proof: A term from logic and mathematics describing an argument from premise to conclusion using strictly logical principles. In mathematics, theorems or propositions are established by logical arguments from a set of axioms, the process of establishing a theorem being called a proof.
The colloquial meaning of "proof" causes lots of problems in physics discussion and is best avoided. Since mathematics is such an important part of physics, the mathematician's meaning of proof should be the only one we use. Also, we often ask students in upper level courses to do proofs of certain theorems of mathematical physics, and we are not asking for experimental demonstration!
So, in a laboratory report, we should not say "We proved Newton's law" Rather say, "Today we demonstrated (or verified) the validity of Newton's law in the particular case of..." Source
Religious belief does not constitute scientific evidence, nor does it convey scientific knowledge.