There's no evidence that Corbyn advocates terrorism or other kinds of violence and he has consistently stated his opposition to violence. If "sympathise" means agree, approve, favourable to, support, Corbyn did openly "sympathise" with the IRA's ultimate goal of a united republican Ireland, but he does not appear to "sympathise" with violence. Corbyn's position is that he wanted to aid the peace process (we can only speculate about his contribution).
But a public relations challenge for Corbyn is that he has historically behaved so as to provide many opportunities to be portrayed as a "terrorist sympathiser" - and not just in relation to the IRA but with Hamas and Hezbollah too. He has also appeared to deny or refuse to acknowledge their terrorist acts. There are patterns of behaviour since his public life began.
It is unclear whether he understands that or is bothered by it but it is clear that many won't forgive him for it.
Corbyn has repeatedly avoided unequivocally condemning IRA violence when asked, choosing instead to condemn the violence on both sides or all bombing, and attended meetings with and vigils for people associated with terrorism. He has referred to these people as "friends", "honoured citizens" and such, rather than neutral terms.
Corbyn met with Sinn Féin's leader Gerry Adams several times during The Troubles in the 1980s. Sinn Féin (rightly or wrongly) considered the political wing of the IRA with interchangable membership and Gerry Adams was alleged (he denies it) to be part of the IRA's leadership - at the very least having some influence. Such meetings were very controversial in that period.
Two weeks after the IRA's Brighton hotel bombing intended to assassinate the Conservative party's leadership, including then Prime Minister Margaret Thatcher, and which killed five people and injured over 30, Corbyn invited Gerry Adams and convicted terrorists Linda Quigley and Gerry MacLochlainn to the House of Commons.
Labour's then Chief Whip Michael Corks commented,
in the present climate of opinion this action must be regarded as
thoughtlessness of the highest order.
Labour's leader Neil Kinnock was said to be appalled and furious.
The meeting was also shortly before the first anniversary of the 1983 Harrods bombing, which killed six people and injured 90.
Corks told the BBC,
I think that, unless you are very very careful, any contact with
people of this sort gives credence to their cause, and unless you are
very careful that can lead to people thinking you are actually
indifferent to the outrage, the suffering, the killing and the maiming
which is the direct consequence of the actions of people who are
Corbyn was unrepentant and said he'd do it again. Gerry MacLochlainn claimed to have visited Parliament several times, as a constituent of Corbyn's, and he was reportedly a regular at Corbyn's constituency office. Corbyn denies meeting anyone in the IRA.
Two months later, the Guardian wrote of Corbyn:
Mr Corbyn and a sizeable number of other left Labour MPs ... will
continue their sordid romantic infatuation with the Provisional IRA.
Mr Corbyn's invitation to two convicted terrorists to meet him in the Commons in
October can be attacked on several grounds. It was a very stupid
political gesture from someone who is an elected member of a party
opposed to terrorism. It was appallingly timed, so soon after the
Brighton hotel bombing. ... We agree with Mr Ivor Stanbrook, the very
right-wing Conservative MP for Orpington, when he says that to stop
the public from meeting their MPs is to play into the hands of
democracy's enemies. But there is a time and a place for everything
and Mr Corbyn has little reason to feel proud of his judgment.