One must remember that persecution can take a variety of forms.
With regards to the headline issue of executions, even Mary’s most eminent academic advocate, Eamonn Duffy, puts the figure for Elizabeth at ‘more than 200’, while implicitly conceding that this doesn’t quite match the traditional figure of 284 for Mary.
But there were other factors involved. As with any figures for punishments inflicted, the enthusiasm by the authorities to carry out those punishments can only be part of the story. The other half of the equation is the number of crimes actually being committed. And that’s still important even if the authorities are, knowingly or inadvertently, prosecuting many people who are innocent. It may simply be that that Mary faced more people she could regard as being heretics than did Elizabeth. Then there’s the complication that both Mary and Elizabeth depended on some of their subjects bringing those heretics to their attention. Are the number of prosecutions a measure of opposition to royal policy or of support? And can’t they be both at the same time? It could be argued that both Mary and Elizabeth were simply following the same policy of executing any of their religious opponents who made a conspicuous nuisance of themselves.
But there was one significant difference. Elizabeth did start off with a policy of de facto leniency but became much harsher during the second half of her reign. To which it can be said that she did so with good reason, as the threats she faced became more obvious over time. But the point that’s uncomfortable from a modern liberal perspective is that, in the long term, those persecutions probably did help entrench Protestantism. Religious persecutions in early-modern Europe had a habit of being rather more successful than we might wish to believe. Which is one reason why a growing minority of academic historians think that, if given a bit more time, Mary’s policies might have worked.
Then there’s the issue of church attendance. It had long been accepted by most people that everyone should regularly attend their local parish church. That was just taken for granted as a social convention. Moreover, the church courts did have some powers to prosecute non-attenders, although the implementation of this was often haphazard, usually depending on other aggravating circumstances. This didn’t really change until Elizabeth’s reign. Again as part of the shift towards a tougher policy, Elizabeth makes non-attendance a criminal offence which could be prosecuted in the secular courts. In theory, this tightened things up. But in practice, much depended on the willingness of local magistrates to act, so its implementation remained notoriously haphazard. A cynical view would be that the main function of the recusancy laws was as a useful outlet to give the more zealous Protestant justices of the peace something to do during times of heightened political tension.
A third issue is that of press censorship. The trend in sixteenth-century England was towards stricter censorship. And that was cumulative. Mary built on Henry VIII’s policies and then Elizabeth built on Mary’s. But this was just part of a much wider trend. All European governments in the sixteenth century feared the explosion in print and all tried, with decidedly varying degrees of success, to control it.
As for Shakespeare’s supposed Catholicism, that controversy has always been driven primarily by Catholic wishful thinking. The Wikipedia article on his religion actually does quite a good job of conveying just how highly ambiguous all the evidence remains.
But why invoke him at all as an example when one can instead point to William Byrd? He really was a high-profile cultural figure who directly received Elizabeth I’s patronage despite being blatantly obviously Catholic. But then contemporaries were always fully aware that Elizabeth herself preferred a more splendid style of worship in the Chapel Royal than was the norm elsewhere.