Abstaining from meats unto idols and fornication is shown in Acts in respects to the Gentiles here
Acts 15:28 For it seemed good to the Holy Ghost, and to us, to lay upon you no greater burden than these necessary things;
Acts 15:29 That ye abstain from meats offered to idols, and from blood, and from things strangled, and from fornication: from which if ye keep yourselves, ye shall do well. Fare ye well.
The eating things sacrficed unto idols is memtioned by Jesus in Revelation here (along with fornication) again here
Rev 2:14 But I have a few things against thee, because thou hast there them that hold the doctrine of Balaam, who taught Balac to cast a stumblingblock before the children of Israel, to eat things sacrificed unto idols, and to commit fornication.
Whereas Paul seems to be addressing these concerns here
1Cr 8:4 As concerning therefore the eating of those things that are offered in sacrifice unto idols, we know that an idol is nothing in the world, and that there is none other God but one.....
He downplays that an idol is anything at all (and that there is no other God but one (I cut it there) because it talked elsewhere how had winked at peoples ignorance in times past concerning idolatry (In Acts 17:30) but was calling all men to repent of these sorts of things and Paul speaks of those not having this knowledge and some still have a conscience of the idol unto that hour in Pauls present time
1Cr 8: 7 Howbeit there is not in every man that knowledge: for some with conscience of the idol ((((unto this hour)))) eat it as a thing offered unto an idol; and their conscience being weak is defiled.
Paul does at least bring in "unto this hour" just as it speaks elsewhere of His sprinkling them with clean water and cleansing them from their idols (speaking to the conscience). They were still were deemed as necessary by the Holy Ghost in Acts 15:28 because of these current practices.
In Chapter 10 even Paul says this
1Cr 10:25 Whatsoever is sold in the shambles, that eat, asking no question for conscience sake:
1Cr 10:27 If any of them that believe not bid you to a feast, and ye be disposed to go; whatsoever is set before you, eat, asking no question for conscience sake.
Dont ask dont tell policy
1Cr 10:28 But if any man say unto you, This is offered in sacrifice unto idols, eat not for his sake that shewed it, and for conscience sake: for the earth is the Lord's, and the fulness thereof:
1Cr 10:29 Conscience, I say, not thine own, but of the other: for why is my liberty judged of another man's conscience?
And not your own conscience but of the other, in both cases (whether in an idols temple) or at a feast it speaks of the conscience of the other (not yours) who knows better that idols are nothing and dont raise those sorts of questions, but how peoples consciences will judge your freedom.
Just buy take out, dont risk it
None of those references discussing eating rats. Its all about eating food where the only question is "was it sacrificed to idols" - not "is it what God calls an abomination in scripture in Lev 11"
Notice that in Lev 11 not only are rats in the "abomination" category so also is diseased meat. Jesus did not die on the cross so that Christians could eat diseased rat carcasses - that is not what the Gospel is about at all.
Lev 11
10 But all in the seas or in the rivers that do not have fins and scales, all that move in the water or any living thing which
is in the water, they
are an abomination to you. 11 They shall be
an abomination to you; you shall not eat their flesh, but you shall regard their carcasses as
an abomination. 12 Whatever in the water does not have fins or scales—that
shall be an abomination to you.
13 ‘And these you shall regard as
an abomination among the birds; they shall not be eaten, they
are an abomination: the eagle, the vulture, the buzzard, 14 the kite, and the falcon after its kind; 15 every raven after its kind, 16 the ostrich, the short-eared owl, the sea gull, and the hawk after its kind; 17 the little owl, the fisher owl, and the screech owl; 18 the white owl, the jackdaw, and the carrion vulture; 19 the stork, the heron after its kind, the hoopoe, and the bat.
20 ‘All flying insects that creep on
all fours
shall be an abomination to you. 21 Yet these you may eat of every flying insect that creeps on
all fours: those which have jointed legs above their feet with which to leap on the earth. 22 These you may eat: the locust after its kind, the destroying locust after its kind, the cricket after its kind, and the grasshopper after its kind. 23 But all
other flying insects which have four feet
shall be an abomination to you.
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Having said all that - the OP topic is not about permission to "eat rats" but is whether Christians can eat animal flesh at all.