I agree that liturgical Christians do not believe in OSAS, but there are many Protestants who do, especially in the USA, so it had to be addressed.
Yes, if we refuse to “take up our cross daily” we deny following Christ for that was his command. Does that mean we do it perfectly? No. Only by the grace of God can we do it at all. But to refuse to do it leads to rebellion, a “why me” attitude that can certainly endanger a person’s salvation by blaming God instead of calling on God in life’s troubles. It can lead to hardening of the heart. This doesn’t mean that we don’t have our moments in which we ask “why me?”, but if we take on that attitude as a life style, it won’t lead to heaven, that’s for sure.