Just for the record, I'm a PhD physicist, graduated from and teach at a major research university, and think both ID and creationism are utterly absurd propositions, repeatedly confounded by observation after observation. Believing in things without evidence, or in the teeth of directly contradictory evidence, is certainly possible for anybody, including physicists who should know better, but it almost invariably involves being brainwashed when they were too young to know better or think critically into thinking that antique scriptural writings had some magical cachet that simply looking at the world and letting it speak for itself does not.
Evidence directly contradicting creationism in physics starts with this little thing called the Law of Conservation of Mass-Energy . This law states in essence that we have never observed the mass-energy content of the Universe being increased or decreased (outside of the tiny transient violation in quantum theory). Ever. Not as far away as we can see with the biggest telescopes. Not as far back in time as we can see with the biggest telescopes. Not in the laboratory. Not in any physical theory that works to explain a whole host of experimental observations not directly concerned with energy. Not in our everyday lives, where I can be confident that the bed in my bedroom is still there when I cannot see it because mass-energy is conserved.
Empirically, there isn't any good reason to believe that anything, ever was created ex nihilo, let alone everything. It's as silly as believing that the dark side of the moon contains a full-featured Disney resort underneath a crater somewhere, just because we haven't looked (yet), or if you think that is too easy to falsify, believing that there exists a full-featured Disney resort on a moon orbiting the fourth planet orbiting Arcturus, or a full-featured Disney resort "in Heaven" (making it really impossible to obtain either positive or negative evidence.
Then (since you bring it up) there is the information theoretic argument. Both creationism and ID sweep under the rug the entire issue of information theory and intelligence and entropy. Here's precisely how idiotic it is:
We observe complex structure in the real Universe. One asserts -- without proof, and rather in contradiction to both everyday observation of a multiplicity of entirely natural complex forms and common sense -- that complex forms cannot occur naturally. To explain them, we invoke intelligence that must have designed/created the complex forms, the basic teleological "watch implies a watchmaker" argument for God. But of course this makes God even more complex, and by the same argument, even more unlikely to have occurred naturally! The hypothesis thus begins with a special exception -- a natural entity, God, is permitted to have infinitely more complexity than any complexity we observe in nature, all because somebody has a hard time believing that complexity in nature can come about without an active intelligence designing it. Who designs the designer?
Entropy is even worse. All of our observations of "intelligence" involve considerable structure and a fairly rigorous state-switching mechanism supported by physical biology and/or electronics. Entropy is (literally) the log of the missing information (to a physicist) and there are theorems concerning energy, entropy, and heat generation in switching mechanisms supporting intelligence. To be able to perceive time at all -- to enable free will, the ability to act on the basis of an uncertain future -- one requires a point of view that has incomplete information. The derivation of the Nakajima-Zwanzig equation for the time evolution of an open (quantum) system embedded in a larger Universe typifies how intelligent agents have entropy bleed into them from an uncertain external universe, and hence can exhibit non-deterministic behavior. God by definition is omniscient, and omniscience sadly directly contradicts both intelligence and free will. God can only choose between alternatives when the alternatives are not certain.
To a physicist, invoking God and an intelligent creater/designer involves hypothesizing an entire META-Universe filled with structure to support the complexity and intelligence of God, one that is self-contradictory in many ways, and in every respect is far more difficult to believe than a simple explanation, supported by an enormous body of empirical evidence, that complexity spontaneously and naturally evolves out of the simple time evolution of the non-sentient observed laws of nature. This is quite wonderful enough, BTW. One doesn't really need to invent an entire mythology outside of this that can never be measured or observed and that can have any properties you like as a consequence.
We could go on -- the enormous amount of physical, historical, and direct observational evidence of evolution occurring. The genetic evidence. The astrophysical evidence. Creationism and ID are absurd given the existing evidence, although an intelligent omnipotent deity could always choose to communicate directly and alter that situation, should they wish to. So far, they haven't.