Is it legal to call someone a pedophile without a conviction?
It depends, as the other answers have explained. I will add that a conviction is not indispensable for referring to someone as pedophile or criminal. What matters is whether the publisher has sufficient, objective grounds supporting his communication(s) that a person committed a specific crime.
Other than pleading guilty, a conviction only means that a jury determined that the evidence sufficiently supports a finding of guilt. But there are instances where a person commits a crime (as reflected by reliable sources) and yet the criminal is not convicted or even prosecuted. That gap could arise inter alia from negotiations with prosecutors (a form of settlement), prosecutorial discretion, or plain corruption.
Consider the matter of Carol Kuhnke, the Michigan judge who in 2016 got busted for illegal possession of narcotics during the investigation of a teenager's drug overdose. Referring to this judge as narco-felon is neither illegal nor actionable defamation, since that label is supported by --at least--:
- a police report (see last page) where the detective
"determined that Carol Kuhnke [...] knowingly possessed Oxycodone at
their residence that was not prescribed to them", and
- a letter by the special prosecutor informing the Michigan
Judicial Tenure Commission that:
I concluded that the evidence supported the filing of criminal charges for the possession of controlled substances that were not prescribed to her.
The prosecutor's decision not to prosecute this judge does not change the undisputed determination/finding that she committed an offense which Michigan law typifies as felony.
Thus, in both this case and the example to which you refer, what would be illegal/defamatory is to convey that the person at issue was convicted. Other than that, the outcome (or lack) of judicial proceedings sometimes bears no relation with the lawful evidence that justify conveying that a crook committed crimes.