Every man, woman and child? Every infant?
Nope.
And even if they do, as long as there is a single person who doesn't, your statement is wrong.
Read TMI, codex and novels
Elves's lower position in society is one of the major social problems of Thedas. It is designed to be so. Elves are - forgive me for my crude comparison - like Jews in RL. Only recently they finally become treated with less racism than before. Prior to that every major religion, every influental race and every powerful nation thought of them as rats.
Elves and quarians are far from such acception. They live in the worst coniditions. Even some slaves in Tevinter live better than city elves. They are not allowed to get a proper education, a high-ranking job, a home outside alienage
Celene tried to change that and was vigourosly opposed by all the nobility
It is true nowadays that hating people for what their ancestors did centuries ago is unfair. But the problem is, the people of Thedas still do what their ancestors did. This is how medieval times worked: a strict social hierarchy with almost no chance of better place for the lowest classes. Elves are the lowest social class in Thedas. Lower can only by vashoths, but they are not even a social class - just outsiders
Shoot, at the height of Arlathan's power, elves treated the lower rung of society much like the humans typically treat the elves of the alienage. They can't even seem to catch a break from each other.
High elves of Arlathan treated lower elves like nobility treats peasants and middle class. Which is natural for any system with hierarchy, unfair, but is still better than what happens between humans and elves