Can such people (who continue to practice sin) frequent our churches and profess to be Christians on the basis of their belief in the crucifixion and resurrection of Christ?
Yes, that is what is called confessing with your mouth and not believing in your heart. They have knowledge of Christ, but they haven't fully surrendered their heart and lives to Him.
If they profess NON-OSAS, works salvation or they don't believe that it's finished at the cross or that future sins are not payed for, then you will know them by their fruit.
Matt 7:15-16 “
Watch out for false prophets. They come to you in sheep’s clothing, but inwardly they are ferocious wolves. 16
By their fruit you will recognize them. Do people pick grapes from thornbushes, or figs from thistles?
Matt 7:22 On that day many will say to me, ‘Lord, Lord, did we not prophesy in your name, and cast out demons in your name,
and do many mighty works in your name?’
2 Pet 2:1
But there were also false prophets among the people, just as there will be false teachers among you. They will secretly introduce destructive heresies, even denying the sovereign Lord who bought them--bringing swift destruction on themselves.
God bless.