I don't see the big deal with it, it's just a big prayer, why does it bother Protestants so much?
1. Rote prayers don't fit the biblical model for prayers. The only such prayers Scripture comes close to endorsing as "rote" are the Psalms.
2. Rote prayers have their roots in tradition. Tradition is not our rule of faith. In the case of the rosary, they are often aren't to God Himself.
"Protestant" prayers are to someone who can actually hear them, God.
3. The Lord's Prayer is not intended to be a rote prayer. It is a model prayer, an outline for the structuring of prayer. Even though the Lord's prayer is prayed by "Protestants" you won't generally see them saying that they prayed 500,000 Our Fathers in order to try to get God to do something."Protestant" prayers do not seek to be effective through vain repetition.
4. Praying the rosary has traditionally fostered
a trust in the rosary itself, not God. Indeed, that fits the biblical pattern. That's why the serpent made by Moses was eventually destroyed.
5. The rosary was allegedly received by St. Dominic in1208 in a vision of the BVM. Protestants aren't followers of the BVM. Indeed, the Marian dogmas have their roots not in Christian Theology, but in Gnostic theology and have been condemned at least twice by two Popes, facts Roman Catholics today generally don't know or ignore. So, in fact, there is no such thing as a consensus of the Fathers with respect to the Marian dogmas, a direct violation not only of the Protestant rule of faith but the Catholic rule of faith as well.
So much for the rosary...
It really wouldn't hurt Roman Catholics (and the Orthodox) to actually do some basic biblical exegesis...religious symbols in the OT that were kept were eventually venerated of themselves, and the people were accused of prostituting themselves for such practices. That's idolatry, in case you need to have it spelled out. So, that's why Protestants find it bothersome. We don't merely find it "bothersome." Those of us who are consistent Protestants find it utterly repugnant. I'll gladly put that statement into the written record. It amounts to using prayer as "word magic." That's a direct violation of the Decalogue's command not to take God's name in vain, for that's what the commandment is referring to. Protestants often do, however, practice a form of word magic themselves by roting repeating the phrase "In Jesus Name, Amen." That's not functionally any different. The instruction to pray in Jesus' name is not an instruction to say a magic phrase at the end of a prayer, rather it means to pray in the character of Christ, in accordance with God's revealed will, etc. There is not one New Testament example of praying a rosary or saying phrases like "in Jesus' name" as part of our prayer lives. Such practices are nothing but superstition wrapped in Christian clothing.