The other three major countries which use First Past the Post at the national level are Canada, the UK, and India.
In the current Canadian House of Commons, there are five parties.
In the current British House of Commons, there are 10 parties.
In the current Indian Lok Sabah, there are over thirty parties.
The US is unique in its “two and only two” party duopoly. FPTP may contribute to that result, but that’s not the sole cause. For instance, note that the other three countries are parliamentary systems, where people can vote for third parties without worrying about “wasting their vote”, as third parties can have influence in government, unlike the unitary executive in the US.
Anti abortion people are really into seeing Roe V. Wade overturned. They would pretty much vote for anyone who says they will appoint judges to do that. They don’t care how many porn stars Trump has banged.
But that doesn’t address the OP’s question: why is power politics more influential in the US judicial selection process than in other countries? All countries have power politics but not all countries have a politicised court system.
That’s not quite accurate. There are certain provisions in the Charter of Rights which can be overridden, using the notwithstanding clause, but it has been used very rarely in the past 35+ years.
Other than those specific provisions, it’s just like in the US: a constitutional ruling can only be overturned by a constitutional amendment, or by trying to get the Court to change the scope of its ruling.
In the two examples Wolfpup gave, same-sex marriage and abortion, the federal government never considered using the notwithstanding clause. In the one case, it fully implemented same-sex marriage by legislation across the country, and in the second, although it tried to pass legislation on abortion, it was defeated in Parliament and no government since then has touched it. The decision and the lack of an abortion law seems to have general acceptance.
And in the case of the firearms registry, an intensely political debate, the SCC unanimously upheld the federal law requiring the registration of all firearms in Canada. The response was a political one: the Conservatives campaigned on repealing the registry, and eventually succeeded in doing so. (Note that this was one of the areas that was not subject to the override clause.)
I think these examples show that the comments on the extreme polarisation in the US are the accurate answer to the OP. It’s not that other high courts don’t deal with significant public issues; it’s that other countries aren’t so polarised as the US is, so there is greater acceptance of the court decisions.
The SCC was involved in the implementation, but it never actually ruled on whether same-sex marriage was constitutionally required.
There were court actions in several provinces that held that same-sex marriage was constitutinally required, but the federal government chose not to appeal those rulings. Instead, it posed three reference questions to the SCC, asking for guidance on its proposal to implement same-sex marriage. The SCC gave a unanimous decision which held that the proposed bill would be constitutional, but explicitly stated it was not ruling on wehter SSM was itsefl constitutionally required. In short, the government accepted the rulings from the lower courts but engaged in the SCC to determine how to implement it.
Interesting side note: Prime Minister Chretien in an interview when he retired, said htat he was surprised by the rulings and would never have thought that the equality clause would have that effect, but he accepted it. The significant point is that Chretien was one of the key drafters of the Charter, including the equality clause. His approach is a rebuttal to the idea of original intent: he didn’t try to say the courts were wrong because they didn’t match his original idea of what s. 15 would do, but accepted that once the Charter was in force, it was subject to interpretation by the courts.
Note as well that that the Chief Justice of Ontario, McMurtry, who wrote one of the key decisions upholding same-sex marriage, was one of the other architects of the Charter. What does it say about the whole idea of original intent when two of the key drafters subsequently disagree on how to interpret their constitutional document?