The word “should” may be too strong. I would probably use “we are not obliged to”.
If you google this question, you would quickly see that there are surprisingly many articles stating that the abolishment of the Sabbath rest is unbiblical and is man-made. Some even blamed the Church and the Roman Emperor for contradicting the biblical teaching. I can assure you that such are not the Catholic view.
A number of things to consider:
First, it is evident that soon after the Pentecost, the early Church celebrated Mass every day, but especially on the day commemorating the resurrection, which was on a Sunday. Sunday observance was widely received without a question, although the first Christians were all Jews and at that time Sunday was a work day. Christian workers could not rest on that day, but would clandestinely find their way to Mass, especially in the evening when they would also have a meal together.
The early Church however did not transfer the Sabbath. Sunday was not called the Sabbath or the new Sabbath, but always the “Lord’s Day”. Perhaps the first to clearly write about this was St. Justin Martyr ca. 120AD.
But the Mosaic Law clearly requires keeping the Sabbath. So now with the Lord’s Day added, do we to have to keep both?
Hebrews 3 & 4 in a way talk about this. It explains that the day of rest originally was the promise of rest given in the Old Testament. Yes, God rested on Sabbath after the six-day creation of the universe, but entering into this Sabbath was only given to the Israelites after God had set them free to be his people. Having the Sabbath rest is a symbol of freedom and faithfulness to the Lord. Only children can rest from work. Slaves have no rest days. And only those who keep the covenant can enter into God’s rest.
But Hebrews 3 goes on to say that the Israelites lost that rest, quoting Psalm 95: “I said in my anger: they shall not enter into my rest.” The old covenant was broken.
Hebrews 4 explains that God then offered a new day, “today”. It is obvious that this “today” refers to Jesus’s redemption, the offer of the new covenant; specifically this refers to Sunday being the new dispensation, the “today” after the Israelites lost the Sabbath rest in the Lord.
In light of that, we can appreciate more when Jesus said, “I am the Lord of the Sabbath.” We don’t rest in the Lord based on a day; we rest in the Lord of the Sabbath. It is for this reason why Jesus almost deliberately challenged the law of the Sabbath day, and how the early Christians quickly transferred their allegiance to Jesus Himself instead of the observance of days.
So, I’m not sure if this is much clearer… But if we mean “keeping also the Sabbath as keeping the day”, then I think Jesus answered your question already. But if we mean keeping the Sabbath as finding rest in the Lord, celebrating His gift of charity in the bonds of love that we have, as well as serving those most vulnerable of our neighbors, then we can certainly do that on the sabbath, but even more especially on the Lord’s Day.