The acronym T.U.L.I.P summarizes five core doctrines of Calvinism concerning salvation. I hope I've summarized them accurately enough for the question's purpose.
T. Total Depravity — The doctrine that fallen man is 'dead in trespasses and sins' to the point of not even being able to accept salvation where such an offer thereof to be said to be possible or made possible in Calvinism.
U. Unconditional Election — The doctrine that God's election is, for lack of a better word, arbitrary, or not based on a condition on the creature—everyone saved is just as worthy of it: that is to say, not worthy at all.
L. Limited Atonement — The doctrine that since the grace of God is irresistible and is beneficial without exception to its recipients, this necessitates that Christ died only for such recipients, whose technical term are the elect.
I. Irresistible Grace — The doctrine that those whom God has elected to receive His grace, cannot resist it—according to Calvinism, any notion of 'resist' it would imply that His grace wasn't powerful enough in the first place, since grace means an action God does to someone, and not a spiritual help (which would naturally be able to be refused).
P. Perseverance of the Saints — The doctrine that if God has elected you, you are not among those that are damned, but of the infallibly saved: therefore it is impossible that you will be lost.
In light of these, how do Calvinists answer the objection that 1 Corinthians 8:11 (among other verses, of course) disproves in a marked way the Limited Atonement and Perseverance of the Saints (but also all of T.U.L.I.P since each point can be said to rely on the truth of the others)?
Here is 1 Corinthians 8:10-11 (NA28; my translation):
ἐὰν γάρ τις ἴδῃ σὲ τὸν ἔχοντα γνῶσιν ἐν εἰδωλείῳ κατακείμενον, οὐχὶ ἡ συνείδησις αὐτοῦ ἀσθενοῦς ὄντος οἰκοδομηθήσεται εἰς τὸ τὰ εἰδωλόθυτα ἐσθίειν; ἀπόλλυται γὰρ ὁ ἀσθενῶν ἐν τῇ σῇ γνώσει, ὁ ἀδελφὸς δι’ ὃν Χριστὸς ἀπέθανεν
For if someone sees you, who know better, sat eating in the temples of idols, will not his conscience, being weak, be emboldened to eat things sacrifices to idols? For by your knowledge he that is weak has been destroyed: a brother for whom Christ died.
This appears to me to invalidate both Limited Atonement and Perseverence of the Saints, since scandal is described as destroying one for whom Christ died.
In the same context, St. Paul writes the following to the church at Rome (Romans 14:14-15, 20: NA28; my translation):
οἶδα καὶ πέπεισμαι ἐν κυρίῳ Ἰησοῦ ὅτι οὐδὲν κοινὸν δι’ ἑαυτοῦ, εἰ μὴ τῷ λογιζομένῳ τι κοινὸν εἶναι, ἐκείνῳ κοινόν· εἰ γὰρ διὰ βρῶμα ὁ ἀδελφός σου λυπεῖται, οὐκέτι κατὰ ἀγάπην περιπατεῖς· μὴ τῷ βρώματί σου ἐκεῖνον ἀπόλλυε ὑπὲρ οὗ Χριστὸς ἀπέθανεν. ... μὴ ἕνεκεν βρώματος κατάλυε τὸ ἔργον τοῦ θεοῦ. ...
I know and am fully convinced in the Lord Jesus that nothing is unclean of itself, but that to him who considers anything to be unclean, for him it is unclean. For if by food your brother is offended, you are no longer walking according to love: do not destroy for the sake of food him for whom Christ died. ... Do not destroy the work of God for the sake of food. ...
Thanks in advance.