I would think that venerating Mary would not be a problem to any Christian who takes the Holy Bible seriously. Please reread Luke Chapter One, Verses 26-56, where the Holy Spirit confirms this through Archangel Gabriel ("blessed are you among women"), Saint Elizabeth the mother of Saint John the Forerunner ("Blessed are you among women, and blessed is the fruit of your womb!"), and the Theotokos herself ("For behold, henceforth all generations will call me blessed.").
Now, the blessedness of Mary is due to a most important thing: she consented to becoming the mother of the Son of God (Archangel Gabriel), as a result of which "...there will be a fulfillment of those things which were told her from the Lord.” (Saint Elizabeth) so that the Theotokos can sing in truth "My soul magnifies the Lord, and my spirit has rejoiced in God my Savior. For He has regarded the lowly state of His maidservant; For behold, henceforth all generations will call me blessed. For He who is mighty has done great things for me, and holy is His name. And His mercy is on those who fear Him from generation to generation."
It may also be useful for you to read the POV of a former campus Crusade for Christ Evangelical minister, now Orthodox Priest Peter Gillquist in a short essay called "Facing up to Mary," at http://silouanthompson.net/2008/06/facing-up-tomary/
. This essay is published as a brochure by Conciliar Press and may be found on other Internet sites. The following article by Frederica Mathewes-Green, who is another excellent source for those who are considering joining the Church, may also be helpful:
"It is hard to see Mary clearly, beneath the conflicting identities she has borne over the centuries. To one era she is the flower of femininity, and to another the champion of feminism; in one age she is the paragon of obedience, and in another the advocate of liberation. Some enthusiasts have been tempted to pile her status so high that it rivals that of her Son. Others, aware that excessive adulation can be dangerous, do their best to ignore her entirely.
Behind all that there is a woman nursing a baby. The child in her arms looks into her eyes. Years later he will look at her from the cross, through a haze of blood and sweat. We do not know, could not comprehend, what went through his mind during those hours of cosmic warfare. But from a moment in the St. John’s account of the Crucifixion we know that, whatever else he thought, he thought about her. He asked his good friend John to take care of her. He wanted John to become a son to her—to love her the way he did.
It is not surprising that those who, in St. Paul’s words, put on “the mind of Christ” would discover that they loved her too. Though we may picture the love of Mary as a medieval development, it actually goes back to the faith’s early days. Those first generations of Christians did not include Mary in their public preaching of the gospel; they did not expose her to the gaze of the world. (Likewise, a celebrity today will object if reporters take photos of his family.) But when believers were gathered together in their home community, there Mary was cherished. As new members were brought into the Body of Christ, they would also begin to share in the love the Christ Child had for his Mother."http://www.frederica.com/writings/the-lost-gospel-of-mary-who-was-she.html