Indeed, Jon. And so far as I know (others may be better informed) there are no universally accepted principles for deciding which 'right' (or freedom) takes priority over the other when there is a conflict; it all depends on the circumstances, or what the law says.

In the case of the couple who wouldn't give a double room to a gay couple, I think the judge said that under English law the right of the gay couple not to be discriminated against trumped the freedom of the boarding house owners not to be forced to condone what they thought was immoral behaviour. In the case of the burqa/niqab,there is a clash between the freedom for Muslim women to dress in ways which they believe they ought to with the freedom for other people to be able to look them in the eye or to recognize their faces.

It may largely depend on the priority society chooses to give to the right to practice one's religion freely. We don't have to take the same line as the French, who in this case may be influenced by the fact that they appear to attach a higher priority than (I suggest) most English people do to the republican concept of laïcité and to social and civic homogeneity.