According to Evangelicals, before the Reformation, who were Christians if “Catholics are not Christians”?

The Apostle Peter told us that many false religious teachers will come from within the church itself.

2 Peter 2:1 (NASB)

But false prophets also arose among the people, just as there will also be false teachers among you, who will secretly introduce destructive heresies, even denying the Master who bought them, bringing swift destruction upon themselves.

On the other hand, it is said by Jesus Christ and his disciples that the church would never be totally apostatized.

Matthew 16:18 (NASB)

18 I also say to you that you are Peter, and upon this rock I will build My church; and the gates of Hades will not overpower it.

1 Timothy 4:1 (NASB)

But the Spirit explicitly says that in later times some will fall away from the faith, paying attention to deceitful spirits and doctrines of demons,

This means that over the span of 1400 years ( From the 2nd century up to the 14th century)there were genuine born again Christians.

Romans 11:1-5 (NASB)

I say then, God has not rejected His people, has He? May it never be! For I too am an Israelite, a descendant of Abraham, of the tribe of Benjamin. 2 God has not rejected His people whom He foreknew. Or do you not know what the Scripture says in the passage about Elijah, how he pleads with God against Israel? 3 “Lord, they have killed Your prophets, they have torn down Your altars, and I alone am left, and they are seeking my life.” 4 But what is the divine response to him? “I have kept for Myself seven thousand men who have not bowed the knee to Baal.” 5 In the same way then, there has also come to be at the present time a remnant according to God’s gracious choice. 6 But if it is by grace, it is no longer on the basis of works, otherwise grace is no longer grace.

Note

A born again Christian is someone who placed his/her 100% complete trust/confidence (faith) on Christ as His God and Savior. They became born again through the Holy Spirit.

Romans 1:16-17 (NASB)

16 For I am not ashamed of the gospel, for it is the power of God for salvation to everyone who believes, to the Jew first and also to the Greek. 17 For in it the righteousness of God is revealed from faith to faith; as it is written, “But the righteous man shall live by faith.”

Romans 6:23 (NASB)

23 For the wages of sin is death, but the free gift of God is eternal life in Christ Jesus our Lord.

Romans 10:9-10 (NASB)

9 that if you confess with your mouth Jesus as Lord, and believe in your heart that God raised Him from the dead, you will be saved; 10 for with the heart a person believes, resulting in righteousness, and with the mouth he confesses, resulting in salvation.

Titus 3:5 (NASB)

5 He saved us, not on the basis of deeds which we have done in righteousness, but according to His mercy, by the washing of regeneration and renewing by the Holy Spirit,

[Answering from the perspective of my Non-Denominational Evangelical Church]

Evangelical Christians give a lot of emphasis on "Born Again Christian". As the Wikipedia article says,

Evangelicals are Christians who believe in the centrality of the conversion or "born again" experience in receiving salvation, believe in the authority of the Bible as God's revelation to humanity and have a strong commitment to evangelism or sharing the Christian message.

Some even believe that Baptism is of no value if you are not born again. This, I think is the main reason why we call ourselves Christians and not Catholics. We believe in reading the Bible personally and having a relationship with Christ personally. Holy Communion and Baptism has little value and we believe that a person cannot be saved by participating in such things.

We also give a lot of emphasis on "Assurance of Salvation" which I think is not heard among the Catholics. We believe that the moment you are born again you have the assurance that you are saved and you will surely go to Heaven unless you fall to sin and cannot reconcile your relationship with Christ again(some may have subtle difference in doctrine at this point). See my questions - Assurance of Salvation in Catholicism, What is the Roman Catholic interpretation of John 3:16?

These things may seem a bit hard to understand for Catholics but if they spend some time with us, they will come to know the contrast differences. We believe in personal experiences and we have strong aversion to anything related to traditions. Because of this we see the Catholics as those who simply follow old traditions without questioning why they do what they do. Catholics may not agree here but that's just how we see them. I think now you will understand why I asked these stupid questions. :) Why do Catholics observe Eucharist every Sunday?, What is the importance of reading Bible personally in Catholicism?, What is the purpose of attending the mass and going to Confession?

Now, as for the term "Christian", there is a lot of misunderstanding among both Catholics and Protestants. It is not only us who misuse this term but even some Catholics are also responsible. I have met some Catholics say that they are Catholics and not Christians. I think they say this because they want to differentiate themselves from us. The same thing also happens to other sects such as Jehovah Witnesses and Mormons. Fighting over who is a Christian and who is not is not very helpful and this should be avoided. If anyone calls himself a Christian, who are we to judge that he is not?

Who were Christians before the Reformation?

This one is hard to answer but simply put, if anyone believe in Christ and is born again, he/she is a Christian. In the first century there was actually no denomination. They all were called Christians.

The disciples were called Christians first at Antioch. (Acts 11:26, NIV)

So, obviously they were the first Christians. However, as we all know, something wrong happened to Christianity. Though Catholics today try to cover it with many excuses or explanations, we strongly believe that the original Church became corrupted. This is why the Reformation happened.

Amongst non-denominational evangelicals, a Christian is often regarded as being synonymous with someone who has been born again (regenerated) a la John 3:3 -

Jesus replied, “Very truly I tell you, no one can see the kingdom of God unless they are born again.” - John 3:3 NIV

They regard regeneration (or 'getting saved') as something that occurs if and only if the person responds in faith to 'the gospel' (cf. Ephesians 2:8-9, Romans 10:9). They reject any sense that a person can be regenerated by a sacramental act such as baptism (as this is 'a work'). Many will concede that it is possible for Catholics to be Christians, but they are not automatically so by virtue of being baptised a Catholic - they are still in need of evangelisation and conversion, something that is unlikely to happen in a church that perhaps downplays it's necessity for the already baptised. Some, on the other hand, will assert that because the Catholic church teaches 'a different gospel', the Catholic church is the irredeemably corrupt 'Whore of Babylon', and that in order to demonstrate genuine repentance and to be assured of their salvation, a Catholic should 'come out of her' (cf. 2 Corinthians 6:17, Revelation 18:4).

See I am a Catholic. Why should I consider becoming a Christian? and Are Catholics Christian? for milder and more extreme expressions of these sentiments respectively.

edit: Regarding historical perspectives, I don't have much to add beyond Curiousdanii's excellent points 2. and 3. other than that the prevailing tendency flowing from the Reformation for doctrine to trump tradition is non-trivial: in other words, whatever has been practiced historically (including defining important words such as 'Christian') is irrelevant compared to defining doctrine (including the definition of terms) strictly in accordance with scripture.