Regarding the policeman, I think that it's fair enough if he wants to request a different assignment. Back when I did bar work in my undergrad days, it was fairly common for people to swap shifts around, e.g. if they had an unfinished essay that was due in, or if the shift clashed with someone's birthday. As long as everyone's happy, and the work gets done, I don't see any harm in it. In particular, if the policeman's senior officer approved the request then that seems like an endorsement that the request was reasonable, so any new policies should start at management level and then trickle down from there. On the other hand, if the policeman had said "I refuse to do it, and you can't make me, neener neener", and his boss went along with it to avoid being perceived as racist, that would be bad.
Some of the more reactionary coverage came from the Evening Standard/London Lite, as per this article, which said: "PC Alexander Omar Basha [...] refused to be posted there". However, that article isn't particularly well-written, so I'm not convinced that their interpretation is accurate. For instance: "One of the first initiatives taken by Sir Ian after taking up the post was to change the Met's log from a handwritten style to a bland type in capitals because it discriminated against short-sighted people." What log? Oh, you mean "logo". Then a bit further on: "PC Basha - in his late twenties and with a neatly-trimmed beard - is understood he has recently taken part in recent anti-war protests." I think they mean to say "is understood to have". Admittedly, I sometimes make spelling mistakes too, but I make an effort to proof-read all of my blog posts, and I'm not being paid for this.
Moving on to the veils case, I was reading this article on the BBC website. They said that "he asks women visiting his surgery to consider removing [the veil]", not that he insists on it. If he was refusing to talk to his constituents unless they followed his dress code then that would be wrong. However, I think that it's a reasonable request to make, and he's given a reason for it. Over at Random Acts of Reality (an ambulance blog), Tom Reynolds has expressed similar concerns (basically saying that it's harder to understand someone in a noisy environment when you can't lip read).
However, not everyone sees it this way. The BBC quote the chairman of the Islamic Human Rights Commission saying that this is selective discrimination on the basis of religion. I don't know anything about that organisation, but they sound like the type of self-appointed "community leaders" that Pratchett wrote about in Thud, who would do the most good by jumping in the nearest lake. Basically, I don't see that it's selective discrimination if you apply the same rule to everyone. I'm sure that I wouldn't be allowed to walk around in a Spider-Man mask all day, and there have been well-publicised cases of people being told to remove hats/hoodies when they go into pubs and shopping centres. For that matter, the rules about motorbike helmets can sometimes seem like a demented version of "Simon Says". If I ride my bike to the nearest petrol station, then I have to wear the helmet while I'm on my way there and back, but I have to take it off when I go inside to pay. "Put it on, now take it off, now put it on again." Dude, will you please make your bloody mind up?! It's annoying, but I go along with it because I can sympathise with the reasons (namely that the cashiers don't want to get robbed at gunpoint). Mind you, I don't know whether Muslim women are asked to remove their veils inside petrol stations; if not, then that seems like selective discrimination in their favour. (Ditto for motorbike helmets in fact, given that Sikhs can legally wear turbans instead.) Actually, if people want to start shouting about their rights (something that always raises my hackles), I wonder how disability issues affect this, e.g. if an MP was deaf and relied on lip-reading?
It's possible that Jack Straw is using the communication issue as a smokescreen, and that his real motivation is to attack Muslims, while ignoring other religious symbols (such as someone wearing a cross on a chain around their neck). However, in the absence of telepathy, I don't think it's particularly helpful to speculate about that. Instead, it's better to take his claims on their own merit. So, if you don't see face coverings as a problem, and you'd be in favour of people wearing balaclava masks at meetings, fair enough. If you think that it is a problem, but that it's outweighed by religious concerns, again fair enough. I disagree with both points, but I can respect them. If you claim that it's offensive for someone to even suggest that you follow the same rules/guidelines as everyone else, I have no sympathy.
And finally, coming back to what I said about dubious grammar, the BBC journalists still have room for improvement. I was amused by the article I read last month about healthy eating: Chips down as school term starts. Quoting from that article: "The Department for Education guidelines mean meals must include at least two portions of fruit and vegetables and deep-fried foods are restricted." I suspect that pozorvlak and totherme will immediately spot the ambiguity in that sentence, as fellow computer scientists! Basically, you can interpret it in two ways:
a) Meals must contain two items of fruit, but vegetables/deep-fried foods are restricted.
b) Meals must contain two items of fruit/vegetables, but deep-fried foods are restricted.
So, C- I think - could do better if they tried...