Clarity wrote: "Heterosexual Christians may jump from bed to bed as long as they remarry and repent."
First, if someone who claims to be a Christian is sleeping around, they need to examine themselves to find out if their salvation is real.
Second, "What shall we to say then? Are we to continue in sin so that grace may increase? May it never be! How shall we who died to sin still live in it?... knowing this that our old self was crucified with Him, in Order that our body of sin might be done away with, so that we would no longer be slaves to sin; for he who has died is freed from sin." Romans 6:1-2, 6-7
According to this text we do not have the freedom to continue in sin because God will forgive.