I wouldn't look to Tommy for a coherent worldview. Apart from anything else, most of his fanbase is online and American, so he pivots to whatever he thinks is going to get him onto the big American podcasts.
Having said that, and bearing in mind Tommy is very unpopular but his last rally was five times bigger than what he normally gets, I think there are lots of people with lots of grievances who, whatever their reservations about Tommy latched onto the opportunity to show their displeasure with the way society is going. Some of that is anxiety over culture/immigration, where religion can be a synonym.
Some of it might even be directly religion related. But I love how real life throws up curveballs.
Large parts of the American left have spent ten years hallucinating that the thoroughly irreligious Donald Trump is going to impose theocracy. He hasn't done it yet, but they get more and more fearful that he's really going to do it this time. Those parts of the British cultural left who take their cues from America - looking at you, Humanist Association - are now hallucinating that Nigel Farage (!) is poised to introduce theocracy in the UK. I don't think this is very serious analysis.
The nearest thing we've had to theocrats in mainland UK politics (Northern Ireland is its own thing of course) is the Christian Peoples Alliance, who have faded from view in recent years but once managed to, er, elect councillors in Newham. Which is not exactly a stronghold of MAGA politics but has quite a lot of African Christians.
Meanwhile the new Home Secretary, Shabana Mahmood, is a Muslim woman who wants to restrict immigration, castrate nonces and end two tier justice. We're in the interesting position where the left is denouncing Mahmood as a racist (!!!) while right wing pundits like Trevor Kavanagh are bigging her up as the leader Labour needs.
Real life confounds Tommy and it also confounds Tommy's critics.