Can I refuse to participate in a profit sharing 401k and forbid any employer contribution under my social security number?

Some companies have what is called "Automatic enrollment." Basically, with in so many days of your hire date they automatically enroll you into the 401k plan and place you in a default investment. You have the option to opt out of the automatic enrollment but, you do not have the option to "forbid" an employer to enroll you. Typically, if you're automatically enrolled and you neglect to opt out, You are not able to withdrawal the funds in the account until you're 59 1/2 years old or terminated. Keep in mind that some companies do automatic enrollment annually and just because you opt out once does not mean that's final. They're required to send you notification in the mail to make you aware of the automatic enrollment, so be sure not to through anything away without reading it.