how to stop people from trying to stick words into the mouth of the Messiah.
First of all nobody ever suggested that the Nicean creed were the words of Jesus.
Second, everybody, from both side of the filioque discussion, agree on the concept of the trinity. Muslims do not, so it would be silly on them to take one side or another of that particular discussion, as they do not accept the idea the issue is based on. In supporting either position they would automatically accept a trinitarian God.
Thirdly the argument has by now largely been settled in any case, and both the Orthodox and catholic theological traditions have agreed to mutually respect the slightly different interpretation of an in any case rather arcane side-issue of the doctrine of the trinity. There have even been efforts to harmonise the positions accepted by both sides, and today it really has become an irrelevance. Interestingly, almost all protestant groups use the catholic interpretation of that question, but not the Anglicans.
In reality, the debate was never really about whether the addition of "filioque" by the pope to the text of the creed agreed by the council was technically correct, it was mostly about whether the pope should be allowed to do what he did.
The orthodox bishops mostly objected to the principle of a pope adding something to a text they had previously all agreed to, as a group. They had on the whole much less problems with what had been added as such. I dare say if the pope had bothered to ask first, the whole discussion had not even happened. He didn't mostly because the phrase had simply been in use for hundreds of years before he sanctioned it. He had a choice of condemning long established practice or accepting it. He chose the second option. The bishops in the East who did not have this tradition, found it rude that they were not asked before.
The reason why the Anglicans rejected filioque is also exactly that: a comment on their view of the authority of the pope.