Road journey from Europe to Mecca?

Unfortunately for someone trying to travel between Istanbul and Mecca, the Ottoman-era Baghdad and Hejaz (Damascus-Mecca) railways are no longer in operation.

Even assuming you are Muslim and can legally visit the city of Mecca, an overland trip between Istanbul and Saudi Arabia is not practical at this time due to the civil war in Syria and instability in Iraq.

Should the situation in Syria improve, then it is fairly straightforward. Drive from Istanbul to Antakya/Kilis/?anl?urfa/Nusaybin and cross to Aleppo. From there, drive through Damascus and then to Amman. Once you are in Jordan, there is a border crossing into Saudi Arabia near the Red Sea port of Aqaba. However, I doubt this will be possible for the foreseeable future due to the fighting in Syria.

Alternatively, you could cross into Iraq from Turkey and travel south by taxi into 'dangerous' Iraq and then onwards into Jordan. Taxi drivers do these kind of trips all the time but even if you arranged for security (or are able to blend in), you'd still need to deal with the fact that the visa issued at the Turkey-Iraq border is not valid in the parts of Iraq not controlled by Kurdish authorities.

The closest to an overland journey you could manage these days would be to use ferries between Greece or Turkey and Cyprus, from where there are ferries to Israel and from there transport to Jordan. Needless to say, there are implications to using this route inasmuch as Saudi Arabia won't let you in with an Israeli stamp in your passport.

Iran is the safest way in Middle East when you want to avoid Iraq, Syria and Israel.

As I said in my answer to Quickest way from London to Dubai without flying?, there is a direct train from Istanbul to Tehran. From there, you can go to Bandar Busher by bus, then take a ferry to Dammam. Finally, you can take a bus to go to Mecca.

In June 2019, there really is not any safe way to do this anymore, unfortunately. Take an airplane to Mecca, which is probably the only permitted way to enter Saudi Arabia on a Hajj visa anyways.

There are only a few ways that can get you from Europe to Saudi Arabia, and none of them is safe at the moment. First of all, of course you should avoid any route that passes through Syria and Iraq for obvious reasons, if you follow international news at all. That rules out the direct route through Turkey and the Levant.

The other way is to enter through Jordan, but there's no safe way to cross into Jordan over land from Europe. You may enter Jordan from Israel, but of course that is not recommended, not to mention that there's no safe way to get into Israel (you can't get in from the Golan Heights or Lebanon, and the Sinai Peninsula isn't safe either).

There are Red Sea ferries from Egypt to Saudi Arabia, but all the ferries depart from ports in the Sinai Peninsula, and travelling to the Sinai Peninsula is surely a bad idea. You might be able (but very unlikely) to cross the Red Sea from the Sudan (or Eritrea, which requires you to pass through the Sudan), but traveling to the Sudan is a pretty bad idea.

Entering from the South (i.e. Yemen) is, again, apparently a bad idea as well. The only other way is to go to Iran first and then cross the Persian Gulf to one of the Gulf States, and then cross into Saudi Arabia.

However, there are two problems with this approach too:

1. tensions in the Persian Gulf are escalating quickly, and shipping through the area is likely no longer safe anymore;
2. this route will involve crossing the Empty Quarter (Rub' al Khali Desert), which is dangerous in another way. There are almost no possibility of supplies in the area, and nature can be quite unforgiving. There are supposed to be buses from the UAE to Saudi Arabia, but service isn't very reliable.