Voters should not expect all politicians to be "perfect" or "normal", Lord Hague said amid pressure for more disclosure of their personal circumstances.
Chancellor George Osborne is the latest senior Westminster figure to find their financial interests under intense scrutiny following the Panama Papers leak.
He published his tax return on Monday after Prime Minister David Cameron took the unprecedented step of setting out his circumstances following the revelation that he benefited from an offshore fund set up by his father.
Labour leader Jeremy Corbyn and London Mayor Boris Johnson followed suit - with shadow chancellor John McDonnell having taken the lead some months previously.
The Chancellor declared £198,738 of taxable income, meaning that he benefited personally from the reduction of the top rate of income tax from 50p to 45p, prompting Labour criticism that he profited at the same time as cutting public services and welfare payments.
Mr Osborne also faced questions over claims that he received a five-figure payout from his family's firm despite it paying no corporation tax for seven years.
The Times said wallpaper firm Osborne & Little - from which he received dividends worth £44,647 - rolled over losses and deferred tax payments so that its bill was zero despite multimillion-pound profits.
Mr McDonnell said the tax summaries published by senior Conservatives were "transparent as dishwater" and left "more questions than answers".
Mr Cameron said he did not believe an expectation of openness should extend to all MPs.
But ex-Tory leader Lord Hague said an "age of greater transparency" would require more and more openness by public figures - on issues such as health as well as finances - and that politics would be diminished if all were found to be squeaky clean.
"If Parliament consisted of people who had the simplest possible personal finances, perhaps all having come through the public sector with no questions of business ownership or dividends ... then you would have a very one dimensional Parliament," he told the BBC Radio 4 Today programme.
"The consequence of greater transparency in tax, in medical records, whatever else it may be among leaders, is that there has to be a maturity in the public debate about those things and a recognition that the circumstances and habits of people who are effective leaders will vary greatly."
Winston Churchill's tax affairs "would have been more difficult to defend in public than Prime Minister David Cameron's", he said of the man widely lauded as the UK's best leader.
And characters such as William Pitt the Younger - whose biography he wrote - had "chaotic personal finances" but were "brilliant at handling the nation's finances".
"Personal circumstances are not necessarily a good guide to how good they will be as a prime minister, a chancellor or anything else," he said.
He went on: "We're going to have to bear those things in mind and not expect everybody to be perfect or everybody to be normal."
Lord Hague cautioned that the new era should be tested "in careful stages" rather than a rush to force all MPs to publish their own records.
Mr Corbyn - whose tax return was submitted late but showed he had no savings on which to pay income tax - has suggested public figures beyond Westminster should also be more transparent.
Mr Johnson's disclosure showed his taxable income over four years was £1,985,901, leaving him with a £916,481 bill.
The Prime Minister, who inherited £300,000 from his father and received gifts worth £200,000 from his mother Mary, said it was "natural human instinct" for parents to want to pass assets on to their children.
He also set out new measures to make it harder for people to hide the proceeds of corruption offshore as he sought to draw a line under the row.
Most British crown dependencies and overseas territories have now agreed to share information in future with UK police and law enforcement authorities.
The Government is providing £10 million for a new cross-agency task force to analyse the information contained in leaks linked to Panamanian law firm Mossack Fonseca.