If your character is an atheist, keep it quiet - punishable by fine, imprisonment and corporal punishment in England and Wales, by death in Scotland. This is only for blasphemy, though, so as long as you don't parade around talking about it you should be OK
Catholics, you would have had a hard time of it, as anti-Catholic laws were intensified in 1700.
After being expelled in 1290, which was repealed, by 1690 only 400 Jews had been readmitted to England. A Hebrew printing press was opened in 1705 and in 1723 they were permitted to own land using an edited oath omitting the 'upon the faith of a Christian' part, but I imagine life was not easy in 1714.