If you believe in such a being [as God] then that conflicts with science as a way of knowing because you are believing in something without reliable evidence to support your belief. Scientists shouldn't do that and neither should any others who practice the scientific way of knowing. Denis Alexander thinks there are other, equally valid, ways of knowing but he wasn't able to offer any evidence that those other ways produce true knowledge.There are several problems with what Prof. Moran says in this paragraph.
1. He conflates knowing and believing. He oscillates between talking about beliefs and talking about knowledge, but knowledge and belief are not the same thing. One must believe something in order to know it, but merely believing something isn't the same as knowing it. You can believe something and not know it, but you can't know it and not believe it.
To be knowledge the belief must be warranted somehow, and it must have a high probability of being true.
2. He assumes evidence is required to justify a belief. That is something he himself apparently believes, but what evidence could he offer to justify believing it? He simply believes this claim without any evidence at all.
Presumably, he means that our beliefs must be supported by sensory evidence, but this is surely false. Scientists as well as laymen hold all sorts of beliefs for which there's no sensory evidence whatsoever.
Many believe, for instance, that life originated purely naturalistically although there's not a shred of evidence that it did or that such an origin is even physically possible. They often seek to avoid the implications of cosmic fine-tuning by promoting the existence of a multiverse for which there's no empirical evidence. They believe that life exists elsewhere in the universe, and spend their careers searching for it, despite the utter lack of any evidence for such life. They believe that it's wrong to falsify data on a scientific paper, but cannot explain scientifically why anything at all is wrong.
Put another way, I can know that I'm experiencing pain even if I have no way to prove it to you; I can know that, despite much evidence against me, I'm innocent of a crime of which I've been accused; I can know that as a young boy I found a dollar bill, though I'd be helpless if asked to present evidence of the fact.
These are all things that I can know despite my inability to produce evidence that I could offer to anyone else, especially to someone predisposed to doubt me.
If Prof. Moran were to reply that I have the evidence of my own internal states, the subjective experience of pain, the assurance of my innocence, the memory of finding the money, and that these states count as evidence, he'd be putting himself in an awkward position. He'd have to explain why these states warrant the relevant beliefs, but the internal assurance one might have of experiencing God does not warrant believing that God exists.
3. He's simply mistaken to assert that there's no reliable evidence to support theism. It's been argued on this site for the past fifteen years that as Pascal said, there's enough evidence to convince anyone who's not dead set against it.
Alvin Plantinga gives a couple dozen arguments for theism among which, in my opinion, the best are certain forms of the cosmological, moral, and cosmic fine-tuning arguments as well as the argument from the contingency of the universe.
I'm sure Professor Moran is a fine biochemist, but perhaps he'd do well to stick to his field and avoid dogmatic philosophical pronouncements.
For a more extended critique of Prof. Moran's argument against Alexander see philosopher V.J.Torley's discussion here.