Why people think things like this, I have no idea. Stealth does not mean "Invisible". It never has, it never will.
And detecting it is nothing special. Iraq was able to do it in the 1980s with mostly 1950's era equipment, and the Serbians did it and shot down an F-117 three decades ago with 1950's era technology. And I have seen it done first hand with 1980s era technology.
Now here is the real reason why stealth is important. For RADAR tracking weapons, reducing the RADAR cross section is key, because the weapons require a minimum return in order to lock on and track the target. Not enough of a return, either the weapon will refuse to lock on (and therefore refuse to fire), or it can lose the target and go into an "auto-seek" mode or simply self destruct. And there are many ways to completely eliminate the capabilities of stealth altogether.
The first and most obvious is by tracking a target visually. This is what was done in 1990-1991 in Iraq, and what would be done if another fighter got close enough to engage with their guns. At that point, all the "stealth" in the world means absolutely nothing. After all, that is only effective against RADAR, not the Mark I eyeball. And as part of STEALTH and other modern aircraft they do have a reduced heat signature, but once again not invisible to heat. So get close enough and a heat seeking weapon can still track and shoot them down.
And there are even differing "levels" of Stealth. When it comes to the US, the best is still considered to be the F-117 ("Hopeless Diamond"). From what I have read, that still has the lowest RADAR cross-section of any stealth aircraft the US has made. But that was also offset by the small and limited weapon payload so it was ultimately retired. Second is the B-2. Still in service, but of limited use in many conflicts because it is a strategic bomber and not a fighter. After that is the F-22. An air superiority fighter, and the most stealthy in use today.
And notice, all of those are "US Only" aircraft. None of the three (even the retired F-117) has ever been exported to another country.
Then at the bottom of that list, the F-35. This is a series of three models of multi-role fighters. And as such there are a great many compromises in the design. As multi-role they perform both air to air and air to ground. It does not excel at either one like a dedicated fighter, but it is a good compromise that can do both. And people tend to forget that there are three different models, each specialized for their role.
Now Israel uses an export version of the F-35A. This is the "Air Force" version, so takes off and lands like a conventional fighter. And in general, is essentially a "More Stealthy" F-16. More stealthy than other multi-role fighters, but not as stealthy as an F-22 or F-117. There is also the F-35B that the Marines use. Far more capable than the AV-8 it replaces, miles above the Soviet Yak-38. Then the F-35C, the CATOBAR replacement for the F-18. And largely sharing the same capabilities of the F-18, but more stealthy. And far and away superior to the Su-33 and related fighters.
But Iran has always had a formidable air defense system. Not only do they import some of the best that Russia sells, but they have also developed their own (based largely on US made systems they owned during their revolution). And there is nothing that makes "stealth aircraft" immune from detection or tracking, it all depends on how they are operated and where those defenses are. That is why Serbia was able to do it with long obsolete technology.