NS,
That’s missing the heart of it I think. It's dogmatic belief, not just belief that's the problem. If, say, I found yoga helpful and thought other people would too so should also live their lives that way there are various things I might do: I might teach an evening class; I might start a blog about it; I might even write a book extolling its virtues. What I wouldn’t do though is to insist on seats in the legislature because of my convictions, special schools set aside in which my unqualified claims would be taught as facts, open door access to media outlets whenever they needed someone to pontificate on subjects about which I had no expertise at all. Nor would I use it to “other” groups of which I didn’t approve (those non-yoga-ists eh? Still, I’ll do my best to bring them to the true light – "hate the sin and love the sinner" and all that).
The primary issue isn’t I think about Christians who make my “skin crawl” (though many do) but rather that Christianity (and Islam, and Judaism, and…) make my skin crawl. “But Auntie Doreen is a god-fearing woman and she’s really nice” I don’t doubt for a minute. What I also see though is grotesque stuff that’s so commonplace, so ingrained that it’s hiding in plain sight and so goes largely unremarked. When that nice Archbishop Welby tells us he’s "struggling deeply with the issue of homosexuality" for example, then my reaction is if you’ll pardon my French is, “well fuck you then.” Who the hell does he think he is even to think that there is “an issue” at all, and how dare he give cover to those who would beat up gay men on the street.
Oh, and while we’re here this is what faith that thinks it knows – really knows – better than “mere” reason does. It gives these people a higher calling than the dull old secular law so if they get the word that a priest is raping children, not a problem – we’ll just move him elsewhere so he can wreck a few more lives. After all, God knows best and has a higher purpose for him right? And if the heat really gets a bit much, still not a problem – we’ll just whip him back to HQ so the local plod can’t reach him at all. Job done!
And there’s more – so much more. I know – let’s convince priests that the sanctity of the confessional is such that, even if someone tells you he’s planted a bomb in a classroom of children set to go off an hour later, you’re still not allowed to shop him. Better to have the kiddies blown to smithereens than to displease my imaginary (but ever so good, honest) god eh?
So no, I don’t admire these people at all. Not because their beliefs are palpably idiotic, but because we privilege those beliefs in public life such that they get taken seriously and so can actually matter. So for every po-faced, holier-than-though, Thought for the Day reading, “I know better than you because I have faith, and I’m am better person too”, minority hating, misogynistic, paedophile protecting, education polluting, science denying, inequality supporting, patronising cleric and their fellow travellers I say “fuck you” too. Disestablish your churches, stop taking tax payer money, re-open as private members’ clubs if you must and we can all point and laugh as we do the flat-earthers.
It's supply and demand. Clearly there is a demand in some parts of society for the religious privileges you mentioned to continue. Non-religious groups in society also seem to have extra privileges and influence - the wealthy, celebrities, people with titles and while enough people exist in society who are ok about letting those privileges and influence continue, not a lot will change.
When there is enough of a drop in the number of people wanting faith schools or when enough people want to reform the legislature etc - when the demand drops, so too will the privileges. It's a bit like Brexit - and change will probably be equally contentious. We have to abide by the outcomes of the democratic process, but thanks to free speech you are allowed to complain about it.
And while we are on the subject of free speech, you can accuse any law-abiding person who expresses any opinion you don't like of giving "intellectual cover" for a third party's criminal behaviour. Your concept of "intellectual cover" seems to be a poorly disguised attack on free speech. In which case I think it is vitally important that I and anyone else who supports free speech continue to give intellectual cover at every opportunity.
The examples you gave about the cover-up of abuse or the sanctity of confession etc can't be used to generalise about every person's faith in action. There may well be many similar examples but given the cover-up of abuse in schools, charities, UN Peacekeeping forces, Hollywood, it seems like covering-up is a human behaviour which can exist with or without religion. These examples can't be used to generalise about every single person who has faith and who is not involved in these kinds of behaviour - to do so just comes across as bigotry on your part. Not that you necessarily need to care that you come across in that way.
ETA - I too could argue that your Islam and Christianity "makes my skin crawl" line provides intellectual cover for children being bullied because they are religious.
https://www.childline.org.uk/info-advice/bullying-abuse-safety/types-bullying/faith-religious-bullying/