I think there is a reasonable explanation for this.
You've almost certainly heard of the Highland Clearances, when thousands of crofters were evicted from their land to make way for sheep, which were more profitable than people. Many of the evicted crofters were sent off, or emigrated of their own free will, mainly to North America.
However not all emigrated. Many were re-settled in villages around the coast, and had to turn from farming to fishing to make a livelihood. Even in parishes where clearance did not take place, there were significant shifts in population as new industries grew and new towns and villages began to develop. This result of this was that in many large parishes there were significant numbers of people who lived too far from the parish kirk to attend services regularly, and this was seen as
A Bad Thing by the kirk and the government.
So the government came up with a scheme to provide chapels-of-ease, that is, additional kirks in such villages. See
http://www.geograph.org.uk/article/Thomas-Telfords-Parliamentary-KirksStrathy was one of the places that got a Parliamentary kirk, in 1828. So from 1828 until Strathy was disjoined
quoad sacra from Farr, the kirk at Strathy was an outpost, if you like, of Farr Parish Kirk.
What I think probably happened is that the minister at Strathy kept a register of baptisms and marriages there, but that he sent his records periodically to the parish minister, and the session clerk for the whole parish duly copied the information into the main parish register.
After Strathy became a parish in its own right, this would no longer be necessary, but for the few years between the building of Strathy Kirk and the erection of the Parish of Strathy, you would get events recorded out of sequence in the Farr Parish Register as a result.
BTW there were no registrars in the 1820s and 1830s. Registrars only came into being in 1855, at the start of statutory civil registration of births, marriages and deaths. They
were and are required to record the place of the child's birth and the residence of the parents if it is different.
The pre-1855 parish records, including the registers of baptisms, banns and burials, were kept by the session clerk. The Kirk Session is the committee of minister and elders who run the affairs of each kirk, and the session slerk is the secretary of the KS. Quite often the parish schoolmaster also served as session clerk.
Some kept better records than others, recording not only the name of the father's name and the date of baptism, but also such details as the child's given name(s), sex and date of birth; the mother's name; the parents' residence; the place of baptism; the names, occupations, and residences of witnesses and their relationship to the child, and even the person after whom the child was named. (Though I have yet to see a baptism record containing all of these details.)