There absolutely is in Classical Hebrew. Which is what we are talking about.
This is not correct—at the very least, I would like to see a cite for that. E.g. your link mentions a clip by a “female from Israel”, but she does not really sound like she spoke Hebrew during the Iron Age.
How do you pronounce “Caesar”? 
You refer of course to the Tiberian Masoretic pronunciation of the begadpekat as fricatives instead of stops. Nowadays it only applies to beth (excuse me, bet), peh, and kaph —making them /v/, /f/, and /χ/, respectively— but for the Tiberian Masoretes it applied to all 6 of those consonants when following a vowel. Babale would presumably also recoil at the sounds of /ɣ/ for g and /ð/ for d. Also, I believe the Tiberian postvocalic kaph would have been velar /x/ instead of today’s uvular /χ/.
Never mind that in Yemenite Hebrew the sounds /ɣ/, /ð/, /x/, and /θ/ are still used. So it’s inaccurate to say they’re un-Hebrew. They’re un-modern Israeli Hebrew, but that isn’t the be-all and end-all of the language.
The change of sh to s is the fault of Greek, though. I’ll give you that one.
So what’s the correct pronunciation of “shibboleth”?
Wouldn’t you like to know, Ephraimite?
Most historians, if they heard “Western Turks,” would think of the Western Göktürk Khaganate, which extended across Central Asia west to the Crimean steppes in the 6th–7th centuries. They allied with the Byzantine Empire against the Sassanid Persians, which weakened Persia shortly before the Islamic conquest. They were succeeded on the Russian steppes by another Turkic power, the Khazars, who have some Judaism in their history, although Khazars are not the ancestors of the Ashkenazim.
https://www.kan.org.il/content/kan/kan-11/p-526767/s6/771417/
It saddens me that very few of you can appreciate this skit 
You’re righter than you know. When I clicked on it, it would not play on my browser.
I got it to play, but not to generate English subtitles.
It’s probably difficult to translate it-- Part of it was exchanging Hebrew tongue-twisters.
That’s too bad! And strange, it works on my phone and on my computer.
That’s annoying, but I’m not sure how funny it would be with subtitles.
The joke is that Yiftach is trying to get Ephraimites to out themselves by showing them a shibboleth and asking them, “What is this?”. Ephraimites would say “sibboleth” instead of “shibboleth”.
First couple guys pass no problem. Then an Ephraimite shows up. He tries to trick Yiftach by identifying the shibboleth as “wheat” or “some kind of grain”, but to no avail. Yiftach asks him to say a modern tongue twister with a bunch of SH sounds (think “she sells sea shells by the seashore”) but the Ephraimite outwits him by teaching him a different tongue twister and, when Yiftach successfully says it, celebrating: “Hooray, now you can pass!”. Yiftach is about to let the Ephraimite through, but he thanks him for teaching him the tongue twister, and the Ephraimite says “you’re welcome”, “bevakasha”, only he says “bevakasa”. Uh oh!
So Yiftach has him seized, but the Ephraimite begs for a moment of their time and starts psychoanalyzing Yiftach. “Are you sure you aren’t mad at yourself, because you killed your own daughter* and because of the internalized trauma of growing up as the son of a prostitute?”. He hits all the usual psychologisy tropes, which is funny because they’re in biblical times and even funnier because now the Ephraimite is dropping multiple SH words every sentence, all pronounced with an S. He asks, “are you sure that you aren’t trying to fill the hole in your heart with corpses?”.
Finally, Yiftach is visibly moved, admitting that he how’s the major work to do on himself. But then he orders the Ephraimite killed anyways. When the Ephraimite is being dragged away and he asks why, Yiftach replies: “because I’m a son of a bitch, that’s why!”. The narrator then tells us that Yiftach killed 42,000 Ephraimites that day, but never did fill the hole in his heart.
*Yiftach earlier falls victim to a classic trope where he says “If I win this battle I will sacrifice the first thing that comes towards me when I go home”, thinking he will see some livestock or a dog, but instead it is of course his own daughter who greets him.
Speaking of butchered names, how the fuck do you go from Yiftach to Jephthah?
And at the time when I read the Witcher books it didn’t click for me that the whole “law of surprise” deal was the same story as Yiftach’s.
Ys always go to Js, and T to Th. F and Ph are usually pronounced the same in English, are you trying to make a distinction? And there’s no Hebrew ch in English, so h is a reasonable substitute.
I did recognize the story in the Witcher. And a bunch of others when i read the book version, where it’s clearer.
I know that it’s the case, I just don’t have to like it 
Hebrew doesn’t even have a J, we do a G (ג) with an apostrophe.
When I see Yiftach, I think יפתח.
“Jephthah”, I think “Gesundheit”.
Yeah, nice try.
That has to do with how in the Latin alphabet I and J were the same letter and they did not start words with “Y” so when the Vulgate Bible was set down the names beginning with “Y” turned into beginning with “I” and over 700 years everyone in the west got used to that spelling and then the late Middle Ages/Early Renaissance comes along and the Western languages come around to “OK, so I is the vowel and J is the consonant” so J it was now on, and when the vernacular translations come up everyone is like “nah, we’ll keep the transposed spelling we got used to.” That dude spent the Middle Ages being named “Iephtae”.
When you grow up around more Yiddish speakers than Hebrew, it’s “Shabbos” anyway.
I’d be happy if I could just get people to understand that “Yochanan” and “Yonatan” are completely different names in Hebrew, so no, my name is just John and it is absolutely NOT short for “Jonathan” and to please stop calling me that.
Is this linguistic snobbery a put-on or are you being serious?
I can’t speak for Babale, but since I started studying Judaism last year, it’s been my observation that people whose Jewish education was rooted in Hebrew (ESPECIALLY Orthodox/Hasidic types, though I don’t believe Babale is one of those) strongly prefer the classical Hebrew versions of Biblical names to the Hellenized-then-Latinized-then-Anglicized versions in modern English Bibles.
I’m much more familiar with the English names myself, so coming at things from the other side of the fence, I tend to get thrown off when I see someone talking about, say, Yirmeyahu, and I have to think for a minute to realize they’re talking about Jeremiah. I can see how it would work the same the other way.
On the flip side, i had an Israeli boss who couldn’t pronounce the American “th” at the end of “Keith”, the nanny of one of my coworkers. I spent some effort trying to convince him that calling the guy Keet would be better than calling him Kees, even if the “s” was closer to the correct sound.