Change the terms you use and leave things open to interpretation - try and meet them halfway
I have experience with a very similar situation as I am a player similar to your friend.
(Note for readers, this section is simply a preamble about my experiences. If this does not interest you, feel free to skip to the next section starting from “Applying this to your world” in bold, after the page break.)
I am not a religious person, I have great respect for and am interested in religions, their history and mythology but I’ve never believed in any religion, I much prefer a scientific understanding of the world.
Why is this relevant? Well because of my beliefs in science over religion, I am opposed to the concept of a higher power creating and influencing the world. So, when a game, or any piece of fiction, forces the idea of “higher beings created the world” upon me, I don’t appreciate it. It’s not an idea I subscribe to and I don’t feel like I should have to alter my beliefs just to be able to immerse myself into a world and fully enjoy a piece of fiction.
Now, this isn’t to say I can’t enjoy fiction with divine beings in it. What I do is rationalise these beings and ideas in other ways. For example, I state that the beings are godlike beings with magic rather than actual gods (which I find to be more realistic in the context of a magic world), or that the religious interpretation is just one possibility and that things can still be explained scientifically or logically (for example, explaining fictional creatures using the Anatomically Correct series on Worldbuilding).
Or, another method I use is to simply ignore the religious side and focus on another part of the game I enjoy. For example, I enjoy God of War, a game focused around gods. The mythology interests me, the story and gameplay are entertaining enough, I just don’t focus on the religious side of it (which is easy enough to do as the game itself does not focus too much on the religious side of the gods, more on the mythological side).
I find that these methods allow for me to better roleplay as my character as, rather than being forced into believing the religion of the world, I can choose not to and use my own interpretations to explain things. If things are left ambiguous or open to interpretation, for example “he might have been a god, or he was simply a powerful wizard or sorcerer”, I find I can roleplay as my non-religious character better, as opposed to being told that “no, he is an actual god, not a spellcaster”.
(For clarification, note that I as a person am fully aware that fictional gods in a fictional world are fictional. However, I as a character in that world would not definitively know if the gods were real or not. When I talk about being forced to believe in the religion of the world, I am talking about myself as my character, not myself as a person.)
Applying this to your question:
I would imagine your friend holds to their religious belief strongly as I do with my scientific belief. As such, I can understand where they might be coming from. They may feel they should not have to alter their belief just so they can play a game.
Additionally, many monotheistic religions punish those who believe in other gods. For example, one of the 10 commandments of Christianity doesn’t allow you to “idolise other gods than myself” (paraphrased). Your friend may feel that, if they accept those gods in your game, they may be punished by their God for doing so. It's unlikely but a possibility. (Also, as an aside, the phrase “don’t idolise other gods than myself“ is itself open to interpretation. It could mean you are allowed to believe in other gods, as long as you don’t worship them). On the other hand though, many followers from monotheistic religions accept the gods of others as being their own God. For example, many Jews and Christians believe they worship the same God as each other, just in different ways - many Muslims accept that the god that Christians and Jews worship is the same one as their God, just they worship them in different ways. So you might suggest that the gods in your world are actually different interpretations of the god and texts they believe in.
If you leave the concept of the gods open to interpretation, your friend may be more accepting of the concept of multiple gods. Your friend has the option of rationalising that “these entities are simply godlike in their power, not actual gods. The only god is their one true God” or “these are not multiple gods, simply people focusing on different aspects of the one true God”.
Or, they could simply try and ignore it, focusing on parts of the game they do enjoy. Although, admittedly, this may be difficult to do if they are in a party with clerics and paladins.
However, I would just like to point out that, as this is all based of my experiences and how I handled it, it may not necessarily work for your player. Personally I am interested in worldbuilding and creating explanations for things, your player may not wish to put in the same amount of leg-work I do just so they can play. If that is the case, you might just have to not play D&D together. However, there are still things you can do to try and meet them halfway.
What you can do:
You do not have to limit the classes or your worldbuilding.
Whilst yes, clerics and paladins are often associated with gods, the actual mechanics of the game focus around dominions, such as life and death, peace and war. Rather than offering gods to believe in, you could offer dominions. Paladins may believe in the oaths they make to themselves and others, which is what gives them their power. There is actually a precedent for doing this in the books. Page 13 of the DMG says this about Forces and Philosophies:
In other campaigns, impersonal forces of nature or magic replace the gods by granting power to mortals attuned to them. Just as druids and rangers can gain their spell ability from the force of nature rather than from a specific nature deity, some clerics devote themselves to ideals rather than to a god. Paladins might serve a philosophy of justice and chivalry rather than a specific deity.
By having clerics and paladins gain the power from slightly different sources, you could keep them in your world but disassociate them from gods. Here and here are videos which explain how you could do this better than I can. I highly recommend you watch them as they cover more things than I could possibly cover here. There are also videos about roleplaying paladins and clerics which you may also find interesting.
As long as there is always the possibility that the god is simply a “man behind the curtain” or they might be different interpretations of the same God, your player may be more willing to accept the game world. Also from the same section on page 13 of the DMG:
it's unusual for a philosophy to deny the existence of deities, although a common philosophical belief states that the deities are more like mortals than they would have mortals believe. According to such philosophies, the gods aren't truly immortal (just very long-lived), and mortals can attain divinity. In fact, ascending to godhood is the ultimate goal of some philosophies.
Again this shows that your ‘divine beings’ don’t have to be actual gods, they may merely be mortals with a lot of power.
I would look to things like Eberron, a D&D setting in which there is more ambiguity about the existence of gods, taking inspiration from that of your own world. Dark Sun is another D&D setting you could take inspiration from, the DMG briefly mentions it on page 10:
In the Dark Sun setting, the gods are extremely distant-perhaps nonexistent-and clerics rely instead on elemental power for their magic.