Methodists and Wesleyans trace to John Wesley. Wesley never believed penal substitution and imputation of righteousness. Penal substitution says Jesus died for sin as a substitute and in a judicial manner, imputing His righteousness to believers. His denial wasn’t scriptural, but logical or practical. He thought penal substitution brought a licentious life, discordant with true conversion. The Wesley denial of penal substitution results in works salvation, also why Wesleyans offer infant sprinkling.
In his catechism, John Wesley wrote: “What is it to be justified? To be pardoned and received by God’s favor into such a state that, if we continue therein, we shall be finally saved.” You can see that if justification does not impute righteousness, someone is not saved at the moment of justification.
Wesley also wrote about faith and repentance: “But must not repentance and works meet for repentance, go before this faith? Without doubt; if by repentance you mean conviction of sin, and by works meet for repentance, obeying God as we can, forgiving our brother, leaving off from evil, doing good, and using his ordinances according to the power we have received.” This explains faith as earned by doing good works. Very confusing, at least.
Finally, John Wesley also wrote: “Are works necessary to the continuance of faith? Without doubt, for many forfeit the free gift of God, either by sins of omission or commission. Can faith be lost for want of works? It cannot but through disobedience.” He taught believers could lose their salvation.