There are several variants to this text. I can't determine which particular variant underlies the NET translation, so it is difficult to address your question completely. Assuming, though, that the NET follows the Greek text shown at Lumina, there doesn't seem to be any disagreement with the Textus Receptus under the King James Version.
The Greek text can be broken down:
7 ὑμῖν οὖν ἡ τιμὴ τοῖς πιστεύουσιν,
To you, therefore, the believing, [is] the honor,
but to the disobeying
λίθον ὃν ἀπεδοκίμασαν οἱ οἰκοδομοῦντες, οὗτος ἐγενήθη εἰς κεφαλὴν γωνίας Psalm 117:22 LXX
[the] stone which the builders rejected, this became [the] head of the corner
8 καὶ λίθος προσκόμματος καὶ πέτρα σκανδάλουcf. Isaiah 8:14 LXX
and a stone of stumbling and a rock of offense
οἳ προσκόπτουσι τῷ λόγῳ
[those] which stumble at the word
εἰς ὃ καὶ ἐτέθησαν
The phrase you are keying in on is the last one. In the phrase εἰς ὃ ἐτέθησαν:
εἰς (eis) is a preposition that is alternately translated as "into", "to", "in", "at", "on", "upon", "by", "near", "among", "against", "concerning", "as", or "as".
ὃ (ho) is a relative (neuter) pronoun
ἐτέθησαν (etethēsan) is a passive form of the verb τίθημι (tithēmi), which is translated sometimes as "appoint", but can simply mean something like "put", "place", or "lay". The tense is aorist, which is a sort of past tense.
Depending on (1) how one interprets εἰς (eis), and (2) what one decides the relative pronoun ὃ (ho) refers to, one can interpret the text in a number of different ways. Many (most?) translations seem to take εἰς ὃ ἐτέθησαν as an adverbial clause modifying the verb προσκόπτουσι ("they stumble") in προσκόπτουσι τῷ λόγῳ ἀπειθοῦντες ("[they] stumble at the word, disobeying"), leading to things like what appeared in Calvin's Geneva Bible:
Even to them which stomble at the worde being disobedient, unto the which thing they were even ordeined.
Modern translations have:
Berean Literal Bible
They stumble at being disobedient to the word, to which also they were appointed.
They stumble because they disobey the word, as they were destined to do.
They stumble because they disobey the message--which is also what they were destined for.
For they stumble because they are disobedient to the word, and to this doom they were also appointed.
An equally valid reading of εἰς ὃ καὶ ἐτέθησαν, however, is to understand εἰς as meaning "regarding" or "concerning", rather than "to". This completely changes the meaning to something like that given in the Orthodox New Testament:
They stumble at the word, being disobedient, in regard to that which they also were appointed.
Only a couple other versions seem to translate the verse in this sense:
Even to those who stumble at the word, not obeying in that for which they were ordained
[Who] stumble at the word, being disobedient to which also they have been appointed
What is interesting is that virtually no one in antiquity seemed to have understood the verse in the sense that most modern translations propose.
Bede, for example, although commenting in Latin was also thoroughly familiar with the Greek text, writes:
They, whom from the very fact that it behooves them to hear the word of God, stumble at the word. They stumble in their mind by being unwilling to believe what they here. He hass exaggerated their foolishness, and added that they do not believe in that to which they also were appointed, because they have been appointed to this, that is, being made human beings by nature, they may believe God and obey His will ... In which they also were appointed is to be understood according to what Paul says in speaking about God: For in Him we live, and move, and exist [Acts 17:28]1
The Greek Oecumenius also seems to read the passage this way, emphasizing man's free will in his commentary on the passage:
God is not to be held responsible for this, for no cause of damnation can come from him who wants everyone to be saved. It is they who have made themselves into vessels of wrath, and unbelief has followed naturally from that. Therefore they have been established in the order for which they have prepared themselves. For if a human being is made with free will, that free will cannot be forced, nor can anyone accuse him who has decreed their fate of having done anything to them which they did not fully deserve as a result of their own actions.2
So if the intent of the author of 1 Peter was to indicate some sort of predestination to disobey or stumble, then we must assume that this meaning was either lost on readers from the very beginning or became lost sometime during the early part of the first millennium and was only later "recovered" sometime after the Reformation.
Another possibility is that the predisposition to stumble arises as a result of disobeying - not as any kind of predestination. I didn't explore this possibility above, but perhaps it would help to harmonize the two possible translations somewhat.
1. Commentary on the Seven Catholic Epistles (tr. Dom David Hurst)
2. Commentary on 1 Peter