Offspring should not have an inherent, stated right to know their biological parents, nor should they be prohibited. This is often a difficult task, for one to decide it's importance, and if it is important to an individual, they should have the right to search, however they should not have some type of inherent right to know their biological parents. A right to know would break down families.
No I do not think that all offspring should have that right. To many times have I personally seen the disasterous affect of a child, or an adult who found there biological parent. People want to assume that a parent is always a positive, however this is rarely the case with an absent parent. It almost always causes more hurt in every way than to just accept that the parent is no longer around. The disappointment, and emotional wounds of that experience would never completely heal.