That's
WRONG.
You cherry picked verses and gave some "quip" someone gave you of "Faith is not faith if there is no obedience"...
You should have read the parts of Romans you failed to quote... I will help you.
Romans 4:4-6
Now to him that worketh is the reward not reckoned of grace, but of debt.
But to him that worketh not, but believeth on him that justifieth the ungodly, his faith is counted for righteousness.
Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works,
That says faith and works are mutually exclusive.
Mouth of 2-3 witnesses (2 cor 13:1)
Romans 11:6
And if by grace, then is it no more of works: otherwise grace is no more grace. But if it be of works, then is it no more grace: otherwise work is no more work.
Again it says faith and works are mutually exclusive.
And one more just for good measure of 2-3 witnesses as in (2 cor 13:1).
Romans 10:13-17
For whosoever shall call upon the name of the Lord shall be saved.
How then shall they call on him in whom they have not believed? and how shall they believe in him of whom they have not heard? and how shall they hear without a preacher?
And how shall they preach, except they be sent? as it is written, How beautiful are the feet of them that preach the gospel of peace, and bring glad tidings of good things!
But they have not all obeyed the gospel. For Esaias saith, Lord, who hath believed our report?
So then faith cometh by hearing, and hearing by the word of God.
Faith cometh by HEARING and hearing by the word of God. Not by obedience... By being told.
Being told and obeying are NOT the same thing.
And now let's tackle the verses you MISQUOTED...
Romans 5:19 is about JESUS the Obedience talked about there is NOT YOURS, NOT MINE... It is JESUS ALONE!
Only Jesus could fulfill the Law. ONLY JESUS! To try to take a verse that shows that ONLY Jesus can fulfill the law, and try to throw people under a law with it... That is WRONG.
Romans 6:16 AGAIN you took it out of context. The verse before is talking about sinning so grace may abound (since sin requires grace). Then Paul is making the argument since we are servants aka slaves, we should obey our new master Jesus, not our old one sin.
Verse 18 for example....
The end of Romans 6 is NOT saying you have to obey to have faith or anything of the sort. It is saying a Christian should obey because they have been freed.
Romans 15:18 you found the word obedient but.... this is obedient to the GOSPEL, not any works after. Read Romans 10:9-13 for more information.
Romans 16:19 is again OUT OF CONTEXT, it is talking about their obedience to doctrine nothing about needing obedience to have faith. Read the two verses before.
Romans 16:26 again OUT OF CONTEXT, verse before Paul says this is according to his GOSPEL, which is given in Romans 10:9-13. The obedience is not to obtain or keep or maintain faith. The obedience is compliance with a command and what is this command? FAITH ALONE.
TO END... Salvation is
FAITH ALONE
If anyone confesses that Jesus is the Lord (God). And believes He raised from the grave on the third day by His own power. And that salvation is FAITH ALONE.
THEY ARE SAVED
No works, no obedience to any rules needed. It is FAITH ALONE.
The only thing required to be obedient to is the gospel I just gave.
1 Corinthians 3:11-15
For other foundation can no man lay than that is laid, which is Jesus Christ.
Now if any man build upon this foundation gold, silver, precious stones, wood, hay, stubble;
Every man's work shall be made manifest: for the day shall declare it, because it shall be revealed by fire; and the fire shall try every man's work of what sort it is.
If any man's work abide which he hath built thereupon, he shall receive a reward.
If any man's work shall be burned, he shall suffer loss: but he himself shall be saved; yet so as by fire.
Salvation is faith alone. Even if a man has not one good work or deed, if they followed the Gospel I gave and Paul gave and ever saved preacher has given... THEY ARE SAVED.
The obedience needed is to the Gospel that Christ did it all and man can add nothing!
If works are needed then Christ died in vain.