I worked with an Israeli Major for a year. He'd fought in both the Six Day and Yom Kippur shemozzles. On the Sinai front in both of those gigs.
In the first one they'd had women serving as front line infantry, but it was a bit of a disaster. No problem with their fitness and ability to fight. The problem was that there was a very deeply ingrained cultural thing which led the male soldiers to takes crazy risks to render aid and rescue to a fallen femme soldier which they would not have done so unthinkingly with a male casualty.
The Egyptians soon learned to plink the female soldiers first, knowing that they could pick off any number of IDF soldiers coming to her assistance. The IDF brass have learned the lesson and although they still have female infantry, the plan is no longer to place them right on the front line in quite such a literal way.
With the Regiment's prime role being to guard airbases, which tend to be behind the front line to some extent, perhaps this is not quite the same consideration.