Why aren't other religions welcome to heaven as well as subject to hell?

You are taking a few verses from Romans and misconstruing Paul's message to the Romans.

So in addition to outXast's answer I would like to add.

Paul specifically made it his mission to take the Gospel to the Gentile World, and we need always remember that when reading his epistles. At the time of Paul the Roman Empire was although not hostile to Christianity (or the way, as the early Church was known) it was only tolerated as a religion of the Jews. The Roman Empire did not begin to persecute the Church until it permeated the Empire, and Rome began to see it as a threat to not only their gods, but their control of the people.

Understanding that is central to understanding Romans. Paul's epistle to the Romans was written somewhere in the time of his missionary Journeys, which began about 50AD. The exact date has never been established. The reason for Paul's epistles was that there was much false teaching going on in the Church at that time.

2nd Corinthians 11:13 through 15 KJV For such are false apostles, deceitful workers, transforming themselves into the apostles of Christ. 14 And no marvel; for Satan himself is transformed into an angel of light. 15 Therefore it is no great thing if his ministers also be transformed as the ministers of righteousness; whose end shall be according to their works.

Many had either misinterpreted the Gospel or had tried to align it with their false gods.

These comments from Jamison Faucett and Brown, may be of some help in understanding the situation.

The Founder of this celebrated church is unknown. That it owed its origin to the apostle Peter, and that he was its first bishop, though an ancient tradition and taught in the Church of Rome as a fact not to be doubted, is refuted by the clearest evidence, and is given up even by candid Romanists.

For What Class of Christians was this Epistle principally designed - Jewish or Gentile? That a large number of Jews and Jewish proselytes resided at this time at Rome is known to all who are familiar with the classical and Jewish writers of that and the immediately subsequent periods; and that those of them who were at Jerusalem on the day of Pentecost (Acts 2:10), and formed probably part of the three thousand converts of that day, would on their return to Rome carry the glad tidings with them, there can be no doubt.

Acts 2:4 through 12 KJV And they were all filled with the Holy Ghost, and began to speak with other tongues, as the Spirit gave them utterance. 5 And there were dwelling at Jerusalem Jews, devout men, out of every nation under heaven. 6 Now when this was noised abroad, the multitude came together, and were confounded, because that every man heard them speak in his own language. 7 And they were all amazed and marvelled, saying one to another, Behold, are not all these which speak Galilaeans? 8 And how hear we every man in our own tongue, wherein we were born? 9 Parthians, and Medes, and Elamites, and the dwellers in Mesopotamia, and in Judaea, and Cappadocia, in Pontus, and Asia, 10 Phrygia, and Pamphylia, in Egypt, and in the parts of Libya about Cyrene, and strangers of Rome, Jews and proselytes, 11 Cretes and Arabians, we do hear them speak in our tongues the wonderful works of God. 12 And they were all amazed, and were in doubt, saying one to another, What meaneth this?

Certain it is, that the apostle writes to them expressly as a Gentile Church (Romans 1:13, Romans 1:15; Romans 15:15, Romans 15:16); and though it is plain that there were Jewish Christians among them, and the whole argument presupposes an intimate acquaintance on the part of his readers with the leading principles of the Old Testament, this will be sufficiently explained by supposing that the bulk of them, having before they knew the Lord been Gentile proselytes to the Jewish faith, had entered the pale of the Christian Church through the gate of the ancient economy.

his declared principle; not to build on another man’s foundation (Romans 15:20) - could he express his anxious desire to come to them that he might have some fruit among them also, even as among other Gentiles:

Romans 1:13 Now I would not have you ignorant, brethren, that oftentimes I purposed to come unto you, (but was let hitherto,) that I might have some fruit among you also, even as among other Gentiles.

This shows Paul's almost obsession with the conversion of Gentiles to the Faith.

So a careful analysis of Romans will tell us that Paul was anxious to visit the Church in Rome, not only to help explain the true Gospel, but to hopefully bring others into the faith.

And we can by careful reading of Romans determine that rather than supporting your concept; what Paul was doing was actually warning against such misadventure. as is exemplified by verses 1:21 and 24 of Romans.

Hope this helps.

Romans 1:21 For although they knew God, they neither glorified him as God nor gave thanks to him, but their thinking became futile and their foolish hearts were darkened. 22 Although they claimed to be wise, they became fools 23 and exchanged the glory of the immortal God for images made to look like a mortal human being and birds and animals and reptiles.

24 Therefore God gave them over in the sinful desires of their hearts to sexual impurity for the degrading of their bodies with one another. 25 They exchanged the truth about God for a lie, and worshiped and served created things rather than the Creator—who is forever praised. Amen.

Those condemned in these verses are not condemned for failing to believe in any higher power, but failing to recognize that there is only one true God and to glorify him. I extended the section to include verses 24 and 25 where it is explicitly stated that worshiping things other than the Creator fails to meet God's standard.

Romans 2:9 There will be trouble and distress for every human being who does evil: first for the Jew, then for the Gentile; 10 but glory, honor and peace for everyone who does good: first for the Jew, then for the Gentile. 11 For God does not show favoritism.

12 All who sin apart from the law will also perish apart from the law, and all who sin under the law will be judged by the law. 13 For it is not those who hear the law who are righteous in God’s sight, but it is those who obey the law who will be declared righteous. 14 (Indeed, when Gentiles, who do not have the law, do by nature things required by the law, they are a law for themselves, even though they do not have the law. 15 They show that the requirements of the law are written on their hearts, their consciences also bearing witness, and their thoughts sometimes accusing them and at other times even defending them.)

My understanding of (one aspect of) this section of Romans 2 is that if you are to be judged based on your works and not based on Christ's redemptive work, then you must fulfill the Law completely. Something that no person has ever done perfectly.

So you have a choice, choose to completely and perfectly obey the Law, as given to Moses. Or accept that Jesus fulfilled the Law and was an acceptable sacrifice to God on your behalf. Since no one can complete the first choice, the 2nd one is the only path to heaven.