A really interesting question since as a Christian who opposes the use of lethal force by Christians, I have tended to count Leo Tolstoy as an ally of sorts since he also takes Jesus' command to 'love your neighbor as yourself' as foundational to an ethic of sacrificial love. However, upon further research (also here) I realized that you are right on the two counts which you ask:
1). As a thoroughly 'modern man' Tolstoy did not believe Jesus performed miracles.
2). Tolstoy also denied that Jesus was a 'son of God' preferring to interpret Jesus' Resurrection as being symbolic and ultimately rejecting his divinity.
On the first count, most Christians in the protestant tradition are willing to be flexible - denial of miracles was all the rage for many in Tolstoy's era and its influence is still evident within the significant 'cessationist' lobby in evangelicalism today. For example, no reference to miracles is made in the Apostle's Creed - although Mary's virgin conception is. On the second count however, Tolsoty is undeniably a heretic having rejected the tenet at the very heart of the gospel.
As my professor at Moody Bible Institute (an institution generally 'reformed' in its thinking) wrote here quoting what is generally considered a standard text of Evangelical orthodoxy:
I am in hearty agreement with Affirmation Ten of This We Believe: “We affirm that the bodily resurrection of Christ from the dead is essential to the biblical Gospel (1 Cor. 15:14).”...Jews and Greeks could conclude that a crucified Messiah is a contradiction, an absurdity. That is, since Jesus suffered and died, indeed was crucified, he must have been rejected by God. But the opposite is the case; the Resurrected One was not rejected by God.
That is the simple answer to your question: if his affirmation of count 1 did not lead to a denial of count 2 (i.e. if he at least affirmed that God the Father bodily resurrected Jesus Christ) then Tolstoy did not belief the Gospel. If he was merely uncertain about this particular point, for example as the exact meaning of what it meant that Jesus was the Son of God, perhaps there could be more conversation and uncertainty as to his status. But since he actively denied Jesus' divinity and resurrection, he stands starkly against the very essence of what Christians proclaimed in the very first sermons in the book of Acts, and against the bare minimum of what all Christians must believe:
...if you confess with your lips that Jesus is Lord and believe in your heart that God raised him from the dead, you will be saved. (Romans 10:9, NRSV)
You close your questions asking about where the 'line' of tolerance is generally drawn, and whether his views can still be viewed as thought-provoking.
In brief, although rejection of miracles is a huge red flag, the last line which all protestant Christians will hold is exactly contention 2 - the bodily resurrection of Jesus - and Romans 10:9 - see also 1 Corinthians 15.
Secondly, although within fundamentalist circles the tendency is never to look beyond the bible for truth, especially in spiritual matters, most Christians of the reformed and protestant traditions are willing to read and learn from a rather wide theological circle. For example, the ethical theme of loving your enemies which so captured Tolstoy and which he identified with the cross has strongly influenced many today, taking Jürgen Moltmann's The Crucified God as just one example.
That Tolstoy looked only at the cross and rejected the resurrection is however, a mark against him that protestants should never forget. It reminds me of the more recent work of open theologian Gregory Boyd's Cross Vision which speaks a lot about looking at Jesus through the lens of the cross at the expense of remembering that the crucified God was raised bodily from the dead.
This raises a final issue relevant to your question, learning from those who reject the resurrection is perfectly acceptable, even recommended for protestants, many of whom work in secular fields, or who find value in reading the work of non-Christian spiritual genius'. However, someone like Tolstoy should not be espoused (from the evangelical perspective) as a 'Christian' teacher or writer, and would never be accepted to pastor or lead within a reformed Church. I think of Jordan Peterson, someone who has recently received praise and attention from American evangelical Christians for his writings about religion (including a 'metaphorical/literary' acceptance of the resurrection) coupled with public calls for him to 'be saved'.