At the beginning of English Civil War, why did Parliament take a hard line with neutrals, thereby effectively helping Royalist recruitment?

I think this is seriously overstating the effects of Parliament's declaration.

King Charles set out from Nottingham with something like five foot regiments on 13 September. It's possible his ranks were suddenly swelled within the space of one week because of Parliament. Given the relatively low speed of transport and communications at the time however, it seems rather more probable that the recruits were already on their way to join him before 6 September.

After two months' recruiting in Yorkshire and the East Midlands he had gathered around him at Nottingham five foot regiments and 500 horse . . . on the 13th September he marched his little army westward.

_{Hutton, Ronald. The Royalist War Effort 1642-1646. Routledge, 2012.}

But either way, this was not most of his forces. The principal means by which Charles raised the royalist army was to issue commissions to regional supporters, authorising them to recruit regiments privately. These were mainly issued in late July and early August. It would have been reasonable for reach regiment to take a month to be assembled. For example,

Lord Paget . . . reached into his own pocket for the money to finance his regiment, and found some of his recruits among his own tenants. He then went further afield, to Lichfield and other places in the south and west of his native county of Staffordshire, to raise men. For his captains he chose a mixture of younger sons of Staffordshire gentry, and gentry from other counties,. By this ramshackle process he put together a regiment within a month.

_{Gentles, Ian. The English Revolution and the Wars in the Three Kingdoms, 1638-1652. Routledge, 2014.}

Thus, when Charles departed from Nottingham in mid-September with some ~5000 men, he did so with the intent of meeting up with the vastly greater force that had already been raised for him in the Marches and Wales. Similarly, when he marched on London on 23 October, he was joined by another three regiments raised in Lancashire, which bumped him up to numerical parity with Essex.

The commissions went out in late July and early August, and by the time he left Nottingham on 13 September they had produced seven or eight regiments of infantry. On his march across the Midlands he was joined y several cavalry regiments . . . and, once he reached Shrewsbury on 21 September, by companies form Wales, the Marches and the north-west.

_{Cust, Richard. Charles I. Routledge, 2014.}

This means that Charles must have already raised a substantial force in the field by the time of Parliament's ultimatum - just not with him personally at Nottingham. So while Parliament doubtlessly miscalculated, the declaration was still not a critical factor in enabling Charles to raise an army, unlike portrayal of the quotes.

The bigger impact is probably that it steeled the resolve of the royalists to fight. For example, in one speech to his troops, Charles reminded them that:

You shall meet with no enemies but traitors, most of them Brownists, Anabaptists, and Atheists; such who desire to destroy both Church and State, and who have already condemned you to ruin for being loyal to us.

_{Hyde, Edward. The History of the Rebellion and Civil Wars in England. Oxford, 1888.}

As for why Parliament blundered in the first place, let's start by examining the declaration Hibbert refers to, which is most likely Parliament's answer to the king on 6 September. The offending passage being:

. . . to the end that those great charges and damages, wherewith all the commonwealth hath been burdened in the premises, since his majesty's departure from the parliament, may be borne by the delinquents, and other malignant and disaffected persons: and that and that all his Majesty's good and well-affected subjects . . . may be repaid all sums of money by them lent for those purposes, and be satisfied their charges so sustained out of the estates of the said delinquents.

This was effectively an indefinite threat hanging over the heads of royalists, who were portrayed in the answer as a disaffected minority. According to Samuel Rawson Gardiner,

Such pretensions could only be made good by overwhelming force, and at this time Parliament had every reason to believe that such a force was at its disposal. On the 7th Portsmouth capitulated to Sir William Waller, and, with the exception of Sherborne Castle, where Hertford still held out, all the South of England acknowledged the authority of the Houses. In the East and in the South, as well as in the Eastern Midlands, there was no sign of reluctance, and in those days the South and East of England contained by far the greater part of the wealth and population of the country.

_{Gardiner, Samuel Rawson. History of the Great Civil War, 1642-1649. Longmans, Green, and Company, 1901.}

Although it doesn't explicitly target neutrals, it's evident that the confiscation threat is likely to compel a hard division of the country. There's no reason to force a confrontation - unless you are confident you'll come out on top. When push comes to shove, uncommitted people are more likely to declare for whichever side is winning. And it seemed to Parliament that they were about to crush Charles.

Thus the reason Parliament miscalculated is simple: they were overconfident.