Tom Bombadil is a good thing and completely fundamental to the Christian elements of the Tolkien world view.

I'm no Tolkien scholar but a few thoughts:

Basically, Bombadil embodies a very Catholic and very Chestertonian paradox. He is one of the most powerful beings in Middle Earth, yet lives an obscure and irreverent life, not getting involved in world affairs.

It is precisely his joy that grants and sustains this power

Bombadil is essentially angelic, drifting between heaven and earth. He is above mortal affairs, intervening only in small things to protect the small and weak.

People wuo kvetch about him not intervening more in the War of the Ring or being more 'badass' miss this central point

His relationship with Goldberry is one of the few sexual elements in the entire trilogy. The natural sensuality of it is reminiscent of the Song of Songs or a few of the stranger Psalms, although their natures puts it above mere lust/ copulation - it is a spiritual union of souls

Taken together, the three Bombadil chapters completely refute the idea that Tolkien was any sort of Nordic crypto pagan:

In the Old Forest, nature in the form of Old Man Willow is seen not as a bounty or a force for humans to harness but as capricious, embittered and dangerous. Old Man Willow is cruel and vindictive, and Bombadil's intervention is necessary to tame it, restoring the natural order

This is men and angels as objects, not subjects of nature - a deeply Christian view, putting us as responsible custodians of creation, not in thrall (or 'harmony' in neopagan terms) to its whims

Fog on the Barrow Downs is a brilliant chapter. In terms of symbolism etc it is basically about the futility of worldly glory

The Barrow Wights were wealthy and powerful in life, and buried with great honour. But now they are prisoners, weighed down by their mortal glories and unable to find ultimate spiritual fulfilment, sleeping on stone among weapons and trinkets that have no use beyond earthly life

They thus also become hateful and vindictive, but are crushed by Bombadil's transcendent spirit, which is joyful and generous where they are petty and selfish. He rescues the Hobbits once again and they go on, with the reader loathing and pitying the wights

A certain type of pagan will say that honour and glory are the only way to attain transcendence. Tolkien clearly refutes this, emphasising the spirit, which is often found in smaller and more everyday objects and acts

The chapters in Bombadil's House, with all the singing and feasting, are less easy to read and do slow down the narrative somewhat.

Nevertheless, they are thematically important.

Small, homely comforts are essential to Tolkien's world view - the Hobbits go on their quest so that their cosy home may be kept safe.

Sharing an island of domestic comfort with a sort of demigod shows the deep spiritual significance of that - the need for home transcends matter

Our God is the God of small things, not a petty sky father obsessed with power and glory but a kind, forgiving, even playful figure of paternal love, whose ultimate plans we cannot know but which we can delight in.

That is what Tolkien believed and it is fundamentally Christian.