"Evangelical Protestants" reject the Catholic approach to venerating Mary, because much of that approach, including defining the Immaculate Conception, the Assumption, Mary's role as co-redemptrix, mediatrix of all graces, and the large number of claimed apparitions, both those officially recognized by the Church, and those not, as being at best, unnecessary for salvation, and at worst, a superstitious human invention. Most Protestants agree that (as Article VI of the Articles of Religion of the Church of England states):
Holy Scripture containeth all things necessary to salvation: so that whatsoever is not read therein, nor may be proved thereby, is not to be required of any man, that it should be believed as an article of Faith, or be though requisite or necessary to salvation.
I've never seen a Catholic reciting the Hail Mary, who 'exclaimed with a loud cry" the quotation from St. John the Baptist's mother that it contains, that is, "Blessed are you among women, and blessed is the fruit of your womb!" Does this mean that Catholics do not treat the Mother of God with the same degree of reverence that Elizabeth did?
The wording of the question (at least) implies that Evangelical protestants treat Mary with insufficient reverence. This raises some questions. First, what is this appropriate amount of reverence to show Mary? Second, what is the evidence upon which this charge is based?
When Thomas responded to Jesus' declaration to his followers that they knew the way he was going, by saying,
"Lord we do not know where you are going, how can we know the way" [John 14:5]
When Jesus responded to Thomas, he said,
I am the Way, the Truth, and the Life. [John 14:6]
He didn't say anything about his mother.
Further, I suspect most Protestants would consider these three passages of scripture, when considering what amount of reverence of the Mother of God is appropriate:
How is it you sought me? Did you not know that I must be in my Father's house? [Luke 2:49]
O woman, what have you to do with me? [John 2:4b];
"Who is my mother, and who are my brothers?" And stretching out his hand toward his disciples, he said, "Here are my mother and my brothers! For whoever does the will of my Father in heaven is my brother, and sister, and mother." [Matthew 12:48b-50]