Yes, BUT-you obviously shouldn't make a big deal about it.
I am not certain whether there is a specific law which bans all Jewish people from entering KSA (probably not, actually), but they definitely won't let you in with Israeli stamps in your passport. As I also have an Argentine passport, I wriggled my way out of that one fairly easily!
You also need a legit reason for entering "The Kingdom". (Business trip/family/citizen). As my Dad works out there, obviously they have to let me in with a residence permit.
Otherwise, there are Tour Companies which specialise in going round all the various ruins etc, and you could join one of those.
I wear a pendant around my neck with the Star of David. I remove this on a friend's advice, every time I fly back to Saudi-it is not a big deal really, but it might get me into a hassle at immigration, and I don't like taking risks.
It is quite a fascinating country if you ever get to come out here, and the locals are most hospitable.
If you find it too much of a hassle to try and "get in", you might want to consider the UAE, which has similar scenery, but no problems with people of Jewish faith.
Hope that helped.
It is a difficult country to get into, but fascinating.
n.b. Just for some background info, I've also been christened!!!
Fortunately, my parents never forced me into any religion, and as a consequence I have respect for all of them. Went to Israel this Xmas-also a fascinating country!!