Culpability of one's defective theology with regards to salvation
I think question #6 is easily misunderstood. Many church goers probably remember their pastors teaching how Jesus is the "firstborn of all creation" (Col 1:15), how "creation is by him through him and for him" (Col 1:16, John 1:3, 1 Cor 8:6) and how the incarnation "began" in a manger at Betlehem (although Jesus as Word pre-existed), so they may have thought that the survey question #6 refers to the teaching above, to which they mistakenly answer "I agree".
Holding defective theology because of ignorance doesn't ruin one's salvation. I don't think this findings is enough to make them "Arian" especially considering
- They are not seminary educated pastors nor are they professional theologians
- They answer the other theological question correctly (#2, There is one true God in three persons: God the Father, God the Son, and God the Holy Spirit) correctly.
In a class final exam, the teacher can presume the students to have learned the material, and can pass/fail a student based on wrong cognitive statement. But salvation is a matter of our heart's alignment with God's heart who IS Perfect Love (cf Great Commandment plus 1 John 4:7-12), helped by correct understanding of God of course, which is why good churches have Sunday school programs for children and adults alike. But going to heaven is not about passing a cognitively-laden test as if before passing to heaven we have to sit down in a classroom being given a sheet full of catechism questions to which we have to have 90% correct. If the adult respondents fail to answer question #6, I suggest it's more due to lacking exposure to good lay theological education in the local churches than an indicator of one's salvation, as God will judge individual's heart, as well as adding an additional criteria for pastors (1 Cor 3:15).
But if the respondents are seminary-trained pastors and theologians who usually have taken a systematic theology course at a Trinitarian seminary (we are presuming this question to deal only with mainstream Trinitarian groups), then YES, if they hold to this position with full conviction and understanding, they are more at risk for losing their salvation because of this false doctrinal belief, which is linked directly to their false understanding of Jesus, which in turn can detrimentally affect their heart's condition before God. Still, it remains for God to judge whether this person goes to heaven. A lot of other factors are in play here, so this "false answer" by pastors / theologians still shouldn't be considered as God's automatic veto, disregarding all other factors such as the quality of one's heart when measured by perfect love.
Anathema and the correct audience
By anathema I think you meant the "formal excommunication by a church", which implies that since they are no longer in the Ark of Noah they will lose their salvation. In the Arian controversy context, this refers to the last section of the Nicene Creed (325):
But as for those who say, There was when He was not, and, before being born He was not, and that He came into existence out of nothing, or who assert that the Son of God is from a different hypostasis or substance, or is created, or is subject to alteration or change – these the Catholic Church anathemizes.
See also the discussion about anathema in chapter 8 of Philip Schaff's often cited book, The Creeds of Christendom: with a History and Critical Notes ((1877).
The potential for pastors and theologians holding false theology to misinform others is the background for the anathemizing language found in Scriptures as well as in the canons of church councils from 4th century to even the 16th century council of Trent. Pronouncing anathema is serious language ([Insert a segment from Truth Unites YouTube where Gavin explained what anathema meant). So the 2 Biblical occurrences in @DanFefferman's answer are for serious matters: correct gospel, and about having love for the Lord.
Why did the council fathers use the language of anathema for those holding the Arian view? I suggest that the main audience was those theologically educated leaders in the church who were at serious risk to teach a wrong understanding of Jesus, which in turn could affect one's salvation among the hundreds-of-thousand of souls divided among flocks, each under a bishop's charge whose main responsibility was to teach. Closer to our time, I suggest that the main audience of the 16th century Council of Trent was also church leaders in the Reformation era whose salvation related teachings (like sola fide) pose a serious risk to lead the (now in the millions) souls to spiritual harm.
Your Q applies for lay individual, not theologically educated church leader, so I suggest this anathema language doesn't apply to those who answered #6 incorrectly. Yes, I would need to substantiate more of that context for anathema, but I hope just by framing it this way is reasonable enough.
Better indicators for one's salvation and positive influence from one's church-going pattern
But the questions below are a lot better indicator of their salvation because they pointed to their believing sola gratia and sola christus, the Biblical teaching for how salvation works. These questions are also a much better indicator of what Jesus means to them personally and functionally. Not surprisingly, Evangelicals "pass" with flying colors:
- #2 (97%): There is one true God in three persons: God the Father, God the Son, and God the Holy Spirit.
- #5 (99%): Biblical accounts of the physical (bodily) resurrection of Jesus are completely accurate. This event actually occurred.
- #14 (93%): God counts a person as righteous not because of one’s works but only because of one’s faith in Jesus Christ.
- #21 (98%): There will be a time when Jesus Christ returns to judge all the people who have lived.
- #33 (99%): It is very important for me personally to encourage non-Christians to trust Jesus Christ as their Savior.
- #34 (99%): Jesus Christ’s death on the cross is the only sacrifice that could remove the penalty of my sin.
- #35 (99%): Only those who trust in Jesus Christ alone as their Savior receive God’s free gift of eternal salvation.
If we now include everyone (non-Evangelicals included) but filter by Attendance (at least once a week), here's the result compared to the general population:
- #2 (94% vs. 70%): There is one true God in three persons: God the Father, God the Son, and God the Holy Spirit.
- #5 (92% vs. 66%): Biblical accounts of the physical (bodily) resurrection of Jesus are completely accurate. This event actually occurred.
- #6 (70% vs. 55%): Jesus is the first and greatest being created by God.
- #14 (78% vs. 57%): God counts a person as righteous not because of one’s works but only because of one’s faith in Jesus Christ.
- #21 (90% vs. 64%): There will be a time when Jesus Christ returns to judge all the people who have lived.
- #33 (86% vs. 56%): It is very important for me personally to encourage non-Christians to trust Jesus Christ as their Savior.
- #34 (89% vs. 64%): Jesus Christ’s death on the cross is the only sacrifice that could remove the penalty of my sin.
- #35 (85% vs. 60%): Only those who trust in Jesus Christ alone as their Savior receive God’s free gift of eternal salvation.
The net effect of church attendance is positive for questions that pertain more closely to salvation than to theology. Question #14 is not as high as other indicators because Catholics don't agree with it. Evangelical pastors looking at this data have their homework cut out for them to include theology lessons in their sermons.
But the result for question #7 (Jesus was a great teacher, but he was not God) is especially troubling, much more troubling than #6, because only God can save you. Only 54% who choose Beliefs:Evangelicals got it right, while those who attended church at least once a week got only 50% vs. 36% for general population. Maybe it's a little comforting that when the filter is both Beliefs:Evangelicals and Affiliation:Evangelical, the correct percentage improves to 71%, and when they are married and attend at least weekly it becomes 78%.