Does Romans 14.5-6 say that the Sabbath can be on any day?

Romans 14.5-6 must be interpreted in context: As for the one who is weak in faith, welcome him, but not to quarrel over opinions. One person believes he may eat anything, while the weak person eats only vegetables. Let not one who eats despise the one who abstains, and let not the one who abstains pass judgement on the one who eats, for God has welcomed him. Who are you to pass judgement on the servant of another? It is before his own master that he stands or falls. And he will be upheld, for the Lord is able to make him stand. One person esteems one day as better than another, while another esteems all days alike.  Each one should be fully convinced in his own mind. The one who observes the day, observes it in honour of the Lord. The one who eats, eats in honour of the Lord, since he gives thanks to God, while the one who abstains, abstains in honour of the Lord and gives thanks to God…I know and am persuaded in the Lord Jesus that nothing is unclean in itself, but it is unclean for anyone who thinks it unclean. For if your brother is grieved by what you eat, you are no longer walking in love. By what you eat, do not destroy the one for whom Christ died.   So do not let what you regard as good be spoken of as evil. 17 For the kingdom of God is not a matter of eating and drinking but of righteousness and peace and joy in the Holy Spirit.  Whoever thus serves Christ is acceptable to God and approved by men.  So then let us pursue what makes for peace and for mutual upbuilding. Do not, for the sake of food, destroy the work of God. Everything is indeed clean, but it is wrong for anyone to make another stumble by what he eats.  It is good not to eat meat or drink wine or do anything that causes your brother to stumble.  The faith that you have, keep between yourself and God. Blessed is the one who has no reason to pass judgement on himself for what he approves. But whoever has doubts is condemned if he eats, because the eating is not from faith. For whatever does not proceed from faith is sin.

Romans 14 is not about the law or Jewish practices.  There is nothing in the law or Jewish practices mandating vegetarianism.  Hence, the Sabbath is not in view.  Another reason why this passage has nothing to do with the Sabbath is that it is about days esteemed by man.  The Sabbath is not a day man esteems; it is a day God esteems.  In Isaiah 58.13, God calls it “my holy day”.

Romans 14 is about eating.  Some ate only vegetables everyday, some ate only vegetables on a certain day, some ate everything everyday.  Paul did not want them to quarrel over this.