Yes, you can give them your social security number or tax number if US resident. Steam accounts have been hacked before so good luck with that.
A few pieces of information that might be relevant:
1) Steam SSN storage stuff is way more secure than most job application storage software is, and tons of job applications out there require your SSN. It's at least on the level of most banks, which requires your SSN to open accounts. AFAIK they've only had a serious hack once, and the encryption on the personal info and credit card stuff was never broken.
2) AFAIK once you put in your SSN it's not viewable again in any way by you, so even if your account is hacked they can't get to it. I'm betting steam support wouldn't even pass out information like that if you needed it, they would just tell you to contact the government.
3) If you were born after 1973 and before June 25, 2011 (assuming you were born in the US) your SSN is totally able to be figured out just from some basic information like where you were born, your name, and a little effort on the end of the person doing the figuring out. It was bad enough that a privacy expert actually came up with a program that could guess your entire social security number from nothing more than basic public stuff in about an hour or two.
I mean sure, don't send it in if you don't want to, but it's literally safer in steam's hands then it is in most of the places that you are going to be required to give it to.
I've already given them mine, personally.