Some Arab countries like Saudi Arabia and UAE are the ones who try to spread this propaganda.
The reason why they do this is that they don’t want their people to somehow support Iran because Iran is the only country that is standing up to Israel with regards to the Palestinian issue.
The idea of being “Secretly Friend” is something that intelligence agencies like the KGB and Mossad like to use. For example, Hamas was created by Mossad at first, so that Hamas could be something like ISIS that could justify IDF policy to crush the Palestinian; just like no one has empathy toward ISIS, they wanted to create the same with Hamas in Palestine.
If Iran was secretly friend with Israel, then that should have been for the purpose of making Israel win and not experience their first ever defeat with Hezbollah.
If Iran was secretly friend with Israel, then Iran should have allowed Assad to fall and Syria gets divided and not the other way around and the same applies for Kurdish referendum in Iraq which could have resulted in Iraq getting divided into three states which would greatly benefit Israel if it was not for Iran.
And again, if Iran was secretly friend with Israel then they shouldn’t have put quite a much of resources to create a local coalition in Iraq and Syria that could defeat ISIS. Indeed the opposite, if Iran was secretly friend with Israel then they should have allowed ISIS to take over Iraq and Syria that resulted in a global hatred and horror for ISIS and Muslim (much greater than the current Islamophobia) which would have legitimised a broad bloody invasion of these countries by NATO and even Israel, which, ultimately, would have greatly served Israel by allowing it to expand and suppress Palestinian while not getting global condemnation.
So, I don’t think Iran and Israel are secretly friends as Israel is doing its best to topple the Iranian government