We may be moving in that direction, but I don't see any of these as a priority. The issue with any institution or organisation is what they have the power and incentive to do and what balances they have to challenge violence and corruption, not whether they believe in any divine forces. There are plenty of secular organisations with people convinced they're doing things for the greater good or just through power can get away with hurting people and I don't see much benefit in just focusing on the religious ones.
I can see removing specific seats in the House of Lords for religious positions, though not removing people just because they are religious leaders. Personally, I'd prioritise strongly reducing and capping the number of MPs who are only there as MP retirement, how can we trust them to be impartial in challenging the government?
I can see removing automatic charity status and putting them on the same level as other venues, but there are many, many entertainment venues - especially ones aimed at families and communities - that have charity status. Many of the art venues in my area are also charities. Many religious organisations do charity work - literally every food bank in my area is connected to religious institutions whether churches or temples and my local Cathedral and art venues gives more support for adult education than the council which has stripped it to dust.
I can see removing the legal requirement for schools to include Collective Worship, plenty of schools already push that law enough and I think it would be great for parents to have the option to have a secular school for their children rather than having to home educate for that. I can also see removing ability for state schools to have family's religion as part of the admissions criteria - this is already Church of England policy to not have that in CoE schools though not all such schools follow that. I don't think we can remove schools being connected to churches, literally. I don't think the UK could afford to either buy the schools where the land and/or building is owned by a religious group or accomodate the schools elsewhere. We have to acknowledge in the UK that many early schools were established by religious groups and we have the legacy from that. I also don't think it would have much benefits nor that it should be a priority in education that is struggling enough.
Distinguishing between organised worship and cultural activities is a lot messier than I think you realise. Even more with religious symbols and dress with cultural symbols and dress and personal symbols and dress. How would you distinguish between my wearing long skirts for personal reasons and another who wears them for religious reasons? How would you address attire for festivals that people celebrate for religious, cultural, and personal reasons? Or clothes with words on them refering to religions, in seriousness or jest? In your regime, would people be allowed to wear Dark Souls shirts?
When people compare all religions to cults or gangs, I can only imagine they've little experience with any of it to try to go for such cheap shock value, ignoring how dismissive it feels to put the vicar down the street who said about Easter "I hope you have a good holiday, if you celebrate..." in the same box as the group who threatened and attempted to kidnap my kids because I'd left as a teenager.
some religions are able to completely disregard laws on equality
The Equality Act and similar legislation all have excemptions in them, and religious organisations are far from the only ones.