First, the immediately surrounding verses of the text in question are significant. From verse 26 to 29, all those laws pertain to avoiding pagan beliefs and practices. Verse 27 is one of those.
Context helps sort out what was meant, as does going by the Hebrew word used in verse 27. From Matthew Henry's Commentary, he shows how (vs. 26) the way the Gentiles used blood was to gather the blood of their pagan sacrifices in a vessel and to identify themselves with demons. Superstitions and horoscopes etc had been seen by the Israelites when in Egypt; they must have no truck with them. Here is his quote regarding verse 27:
"There was a superstition even in trimming themselves used by the
heathen, which must not be imitated by the people of God - You shall
not round the corners of your heads. Those that worshipped the hosts
of heaven, in honour of them, cut their hair so as that their heads
might resemble the celestial globe; but as the custom was foolish
itself, so, being done with respect to their false gods, it was
idolatrous." Commentary, Matthew Henry, p 137 columns 2 & 3,
He then deals with other pagan customs, such as for the dead - cutting one's flesh, and marking one's body, also with prostituting one's daughter in pagan rituals. All these practices were of the one cloth - and had to be cut completely out of the people of God. So verse 17 is to be understood in that context - pagan customs.
Another commentary makes this observation about the verse in question:
"27 not round the corners of your heads: i.e. to cut round, so as
to have a tuft of hair, like the Canaanitish priests. Cp. Jer. 9:26;
25:23; 49:32. corners of the beard = whiskers, as Egyptians did. Cp.
Gen. 41:14." The Companion Bible (study notes) p161, Bullinger
Publication Trust, 1974 reprint
There was no overt pagan association with making straight hair curly, or coiling it into ringlets any more than there was of making curly hair straight. The Hebrew word that has been taken in the LXX to mean 'curl' is naqaph in Young's Concordance, and means 'To go or compass round about'. That might lend itself to the idea of straight hair becoming 'round' in the sense of curly. But in paganism of the day, the emphasis was on cutting off hair in certain ways.
For Christians today, modesty in appearance and apparel is encouraged, but there is simply nothing said about making straight hair curly (or vice versa).