There's a TL;DR at the end (before references), but I thought I'd go through it more in-depth first.
Currently, the Mulhorandi Pantheon is set to only accept the worship of Humans, Half-Elves, and Half-Orcs. I assume this is because these races have traces of human blood within them. I would posit that we should extend this to Tieflings if we want to keep the restriction (but in one case, Set, I'd actually argue that just removing the restriction would work just as well, more below on that).
Fully 2% of Mulhorand are planetouched of some fashion (chiefly Aasimar and Tieflings). This is because Mulhorand has a habit of having living God-Kings ruling it, and their extended families (such as the Houses Helcaliant and Ramathant, which also lend the Thayan names to the gods Horus-Re and Anhur whom they descend from) serving as priests and bureaucrats. Indeed, from a very orthodox position, ONLY people directly descended from the God-Kings can be their priests and only those priests can hold important governmental positions.
Basically, the reason why there are so many planetouched in Mulhorand is because the God-Kings (eg. the Mulhorandi Pantheon) intermingled with local elites and seeded them into the world. It would then be highly irregular to assume that these people bearing the evidence of the God-Kings in their veins would be shunned from their worship, especially since they'd most likely be of the divine Houses such as Helcaliant. Furthermore, a planetouched (including a Tiefling in Thay) is, for all intents and purposes, just a human being who happened to mutate due to the presence of extraplanar blood in their family line. Usually both of their parents are humans, and any kids they'll have will also be human, since planetouched-ness tends to skip generations.
Finally, in the case, of Set in particular (the one Mulhorandi god who, under the name of Typhon, is actually socially acceptable to worship in Thay since he opposes the rest of the pantheon) his church very explicitly welcomes far more worshippers than is common for the pantheon. Although I am unsure if the line "the clergy of Set was composed of evil beings from any ethnicity" on his wiki page refers only to Human ethnicities, it nonetheless should be all rights include Tieflings (especially Tieflings directly descended from him) since they don't exactly magically have a different ethnicity from their birth parents. In case the line refers to also non-human ethnicities (which there is evidence to support, as he is worshipped as Zehir by the yuan-ti) you could honestly just remove the restriction.
TL;DR
Priests of the Mulhorandi gods are always from the gods own extended family, except in the case of Set
There are many planetouched in Mulhorand specifically because the gods intermingle with the populace
As such, most planetouched are directly descended from the gods, it is weird that they can't worship them
Planetouched usually have two human parents, and will have human children. They're more of a mutation.
Planetouched raised in a human culture will take on that human culture, their ethnicity is the same as their parents.
I'd argue, as a result, that planetouched are if anything more "human" than half-orcs or half-elves.
https://forgottenrealms.fandom.com/wiki/Horus-Re
"The position of priest in the church of Horus-Re was hereditary; members belonged to the House of Helcaliant, and could claim at least one divine incarnation of Horus-Re among their ancestors."
https://forgottenrealms.fandom.com/wiki/House_of_Helcaliant
"As with all organizations of the Mulhorandi pantheon, positions of power within the priesthood were typically hereditary and most priests were descendants of various incarnations of their god."
https://forgottenrealms.fandom.com/wiki/Tiefling
"Although their evil ancestors could be many generations removed, the taint lingered."
"Some tieflings were not descended from mere fiends at all, but from powerful gods."
"In Mulhorand, the most common tieflings were often those spawned from a union with Set or Sebek."
Agreed. With a bit of exaggeration, the current status quo is a bit like if the Church of Lolth in Bezantur barred a drow petitioner from advancing beyond lay member on the grounds of not being sufficiently human.
There's a TL;DR at the end (before references), but I thought I'd go through it more in-depth first.
Currently, the Mulhorandi Pantheon is set to only accept the worship of Humans, Half-Elves, and Half-Orcs. I assume this is because these races have traces of human blood within them. I would posit that we should extend this to Tieflings if we want to keep the restriction (but in one case, Set, I'd actually argue that just removing the restriction would work just as well, more below on that).
Fully 2% of Mulhorand are planetouched of some fashion (chiefly Aasimar and Tieflings). This is because Mulhorand has a habit of having living God-Kings ruling it, and their extended families (such as the Houses Helcaliant and Ramathant, which also lend the Thayan names to the gods Horus-Re and Anhur whom they descend from) serving as priests and bureaucrats. Indeed, from a very orthodox position, ONLY people directly descended from the God-Kings can be their priests and only those priests can hold important governmental positions.
Basically, the reason why there are so many planetouched in Mulhorand is because the God-Kings (eg. the Mulhorandi Pantheon) intermingled with local elites and seeded them into the world. It would then be highly irregular to assume that these people bearing the evidence of the God-Kings in their veins would be shunned from their worship, especially since they'd most likely be of the divine Houses such as Helcaliant. Furthermore, a planetouched (including a Tiefling in Thay) is, for all intents and purposes, just a human being who happened to mutate due to the presence of extraplanar blood in their family line. Usually both of their parents are humans, and any kids they'll have will also be human, since planetouched-ness tends to skip generations.
Finally, in the case, of Set in particular (the one Mulhorandi god who, under the name of Typhon, is actually socially acceptable to worship in Thay since he opposes the rest of the pantheon) his church very explicitly welcomes far more worshippers than is common for the pantheon. Although I am unsure if the line "the clergy of Set was composed of evil beings from any ethnicity" on his wiki page refers only to Human ethnicities, it nonetheless should be all rights include Tieflings (especially Tieflings directly descended from him) since they don't exactly magically have a different ethnicity from their birth parents. In case the line refers to also non-human ethnicities (which there is evidence to support, as he is worshipped as Zehir by the yuan-ti) you could honestly just remove the restriction.
TL;DR
References
https://forgottenrealms.fandom.com/wiki/Mulhorand "planetouched 2%" in "Races" infobox. "The government was run by the clergies devoted to the deities of the Mulhorandi pantheon."
https://forgottenrealms.fandom.com/wiki/Horus-Re "The position of priest in the church of Horus-Re was hereditary; members belonged to the House of Helcaliant, and could claim at least one divine incarnation of Horus-Re among their ancestors."
https://forgottenrealms.fandom.com/wiki/House_of_Helcaliant "As with all organizations of the Mulhorandi pantheon, positions of power within the priesthood were typically hereditary and most priests were descendants of various incarnations of their god."
https://forgottenrealms.fandom.com/wiki/Tiefling "Although their evil ancestors could be many generations removed, the taint lingered." "Some tieflings were not descended from mere fiends at all, but from powerful gods." "In Mulhorand, the most common tieflings were often those spawned from a union with Set or Sebek."
https://forgottenrealms.fandom.com/wiki/Set "The clergy of Set was composed of evil beings from any ethnicity, a practice which came about only after the Godswar."