Hmm… interesting… clearly you think “venerating” is the same as “worshipping.” Is it possible to show special honor without worshipping? Where would you personally draw the line?
Here's my opinion about the "veneration of Mary" shown by Catholics and others: if it walks like a duck and quacks like a duck, it's a duck. A lot of people who worship Mary say they don't, but in their actions, they are giving her far more praise and honor and glory than are due to a person, even someone like Mary who is unique in all of history.
This is from an online Catholic encyclopedia:
This attitude [toward the "worship" of Mary -- and they actually use the word "worship"] becomes still more explicit in Tertullian and St. Cyprian, and the stress laid upon the "satisfactory" character of the sufferings of the martyrs, emphasizing the view that by their death they could obtain graces and blessings for others, naturally and immediately led to their direct invocation. A further reinforcement, of the same idea, was derived from the cult of the angels, which, while pre-Christian in its origin, was heartily embraced by the faithful of the sub-Apostolic age. It seems to have been only as a sequel of some such development that men turned to implore the intercession of the Blessed Virgin.
The (Catholics) have suggested that Mary's obedience undoes Eve's disobedience -- that she is a "substitute" for Eve in the same way that Christ substitutes for mankind in Adam. This is typical of Marian devotion -- ascribing to her the same salvation-related characteristics that the Scriptures ascribe to Jesus. Sinlessness is another one -- that Mary was born without sin, that HER mother (traditionally called "Anna") was a virgin when she was conceived. She's also frequently called "Co-redemptrix" and "co-mediatrix" with Christ. Eep. You can call that "just veneration" if you want, but saying that Mary is fully co-operative in REDEMPTION?? That's worship, and it's also blasphemy.
Here's a link to a set of actual prayers to Mary (the Virgin of Fatima) written in the 1980s. (Most RCs don't take it this far, but it's there, and more common in Latin America.)
As far as where the line is? Here's Martin Luther's opinion, which I can get on board with in general:
She is the highest woman and the noblest gem in Christianity after Christ ... She is nobility, wisdom, and holiness personified. We can never honor her enough. Still, honor and praise must be given to her in such a way as to injure neither Christ nor the Scriptures.
If our honor of her puts her on the same level as that of Christ, that's a major issue. If we're giving her salvific powers, that's a blasphemy issue. No one can save but God. The Scriptures say that Christ is out intercessor before God, and that the Holy Spirit intercedes for us in prayer. It says nothing about Mary. That's significant to me. She was a woman to be honored as one who obeyed God, whose very body was host of the Redeemer of the World -- HUGE deal. I want to imitate her, to set her as an example of joyful obedience in hardship and suffering, and even to recognize her as uniquely and spectacularly blessed! Our Lord loved her as his mother. So far, so good. But the minute we start saying she was perfect, she works together with Jesus to save us, she has the power to answer prayers or to influence God's will... that's when we've taken it WAY too far.