Proper mechitzos in shul was something the Rebbe had to fight for in America of the 50s. Some tried cutting corners with various half partitions, but the Rebbe only pointed out that such a mechitza was a “joke” and defeated its purpose.
One of the early battles of the Rebbe was for the installment of proper mechitzos in shuls. Some chassidim were encouraged to be active on this front, while others were directed to leave a rabbinic or chazan position when improvement wasn’t possible.
In one sharp response from 20 Kislev 5720 (1959), the Rebbe addressed a case where the top half of the partition was made of glass: “They are making a joke out of themselves; who do they think they are fooling?”
In another instance, someone asked the Rebbe how high a mechitza should be.
The Rebbe responded, “A mechitza should be a partition, in the literal sense. A person standing his full height should not be able to see what is happening in the women’s section, as this is one of the reasons that a mechitza is necessary.”
(Teshurah Simpson, Tammuz 5768)
From The Weekly Farbrengen by Merkaz Anash