Rabbi SZA held (in I believe Meorei Eish) that electricity is only assur (on Shabbos) because of minhag aveiseinu.
I have trouble believing this, as a general statement. I plan on looking this up.
Why? because electric lamps (in the time of RZSA) were Aish - fire, according to everybody.
I did hear from The Shmirath Shabbat K'Hilchato - Rav Neuwirth זצ"ל - in a Shiur in the 1980's that he said that RSZA said that if it were not for the stature of the Chazon Ish, he would argue that electricity is not forbidden because of Boneh-building.
So if you get rid of the Bone and the Aish and no other Issur is involved, then that use of electricity could possibly be permitted.
Nothing about Minhag Avosainu. Maybe. See further:
Double AA also says that he heard orally that Rabbi SZA held that certain keilim are only assur because of a similar minhag.
For the record, DoubleAA wrote the following:
Eh. I respect your sourcing this, but I completely disagree with the metziut then. I heard orally in the name of R ShZ Aurbach that indeed there is no real reason to kasher certain keilim which are obviously clean, but we do it anyway because of a minhag avoseinu of equivalent level to minhag avoseinu of electricity on shabbat. I have also heard from different people that R H Schachter has joked a number of times about how all the rabbis should just get together and permit stainless steel as kosher. Even if there are blios in the pot, it seems they are so small to be halachikly negligible. – Double AA♦ Feb 14 '13 at 18:53
Again, this is not what I heard from his very close disciple.
More to the point:
However, why is this not a minhag shtus/foolish minhag
Because if great Rabbis didn't think so, then it isn't.
A Minhag Shtus has no basis in Halacha. Forbidding electricity has a basis; Boneh according to the Chazon Ish. And maybe "let's not confuse people between Aish electricity and cold electricity and forbid it all" or whatever reasoning the Rabbis of yore had.
EDIT if it only began because people believed/held its assur (in regard to electricity) according to Rav SZA.
No. They asked there Rabbis, probably over 100 years ago, and those Rabbis decided it wasn't Shabbosdik.
Oh, and how right they were. What would Shabbos Kodesh look like if we could use our phone, cellulars, boom-boxes and what not.
Is he saying this (electricity minhag) is LIKE a minhag aveiseinu that we should still do it but don't really have to?
Why do you think that a Minhag Aveiseinu is something we do but don't really have to?
Yom Tov Sheini is the classic Minhag Aveiseinu and Chazal have some very harsh words for people who think we don't really have to keep it.
Or is it actually binding, and if so why?
Firstly, as I quoted, RSZA apparently said that he didn't have the authority/guts/foolishness to argue with the Chazon Ish. You can't simply discount the Chazon Ish, especially since a lot of electric appliances nowadays rely on opening and closing of circuits. (Again: Amazing how much foresight the Rabbis of yesteryear had.)
Secondly, as we learn in Shas, the Rabbis had a habit of not informing the public of the real reasons behind their decrees, for at least a year. So it's possible that this isn't a Minhag, but a decree whose reason we don't know.
Lastly, we know that Minhag Yisroel Torah. We also have cases where Minhag trumps Halacha. So, we don't know why, but we still have to do it.
RSZA wrote a lot about electricity. I suggest we all learn those pieces and find what he really said, instead of relying on rumours and memories from decades ago.