No, Christians should not worship Mary.
Worshiping Mary would make her a God.
Exodus 20:3, “Thou shalt have no other gods before me.”
Matthew 4:10, “Then saith Jesus unto him, Get thee hence, Satan: for it is written, Thou shalt worship the Lord thy God, and him only shalt thou serve.”
Study these scriptures: Luke 1:28-38, 42, 48.
28 “And the angel came in unto her, and said, Hail, thou that art highly favoured, the Lord is with thee: blessed art thou among women.”
29 “And when she saw him, she was troubled at his saying, and cast in her mind what manner of salutation this should be.”
30 “And the angel said unto her, Fear not, Mary: for thou hast found favour with God.”
31 “And, behold, thou shalt conceive in thy womb, and bring forth a son, and shalt call his name Jesus.”
32 “He shall be great, and shall be called the Son of the Highest: and the Lord God shall give unto him the throne of his father David:”
33 “And he shall reign over the house of Jacob for ever; and of his kingdom there shall be no end.”
34 “Then said Mary unto the angel, How shall this be, seeing I know not a man?”
35 “And the angel answered and said unto her, The Holy Ghost shall come upon thee, and the power of the Highest shall overshadow thee: therefore also that holy thing which shall be born of thee shall be called the Son of God.”
36 “And, behold, thy cousin Elisabeth, she hath also conceived a son in her old age: and this is the sixth month with her, who was called barren.”
37 “For with God nothing shall be impossible.”
38 “And Mary said, Behold the handmaid of the Lord; be it unto me according to thy word. And the angel departed from her.”
Luke 1:42, (Elizabeth to Mary)”and she spake out with a loud voice, and said, Blessed art thou among women, and blessed is the fruit of thy womb.
Luke 1:48 (Mary speaking) “For he hath regarded the low estate of his handmaiden: For, behold, from henceforth all generations shall call me blessed.”
Some people worship Mary and pray to Mary because of these scriptures.
This should not be so. Christians are to worship God and serve Him only.
Luke 11:27-28 shows that we are not to worship Mary.
27 “And it came to pass, as he spake these things, a certain woman of the company lifted up her voice, and said unto him, Blessed is the womb that bare thee, and the paps which thou hast sucked.”
28 “But he said, Yea rather, blessed are they that hear the word of God, and keep it.”