I am wondering if there are any good examples of acronyms that are not initialisms which contain no vowels.
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I can think of two examples. One is BP or BPS, which stands for "basis point" or "basis points", used in reference to rate changes in a financial instrument or the difference between two interest rates. They are pronounced, respectively, "bip" and "bips".
The other example is "Tcl", for "Tool Command Language", a scripting language commonly used for rapid prototyping, scripted applications, GUIs, and testing. It is pronounced "tickle" by most users.
I think these examples meet your criteria.