It’s true that in PR systems there are always extreme right mps which is horrible if you’re an immigrant or woman or gay or whatever it is they hate in that place, but there are also extreme lefts and you end up with a bit of a balance with either a centre right or centre left in power.
Not necessarily. The example of Ireland's single transferable vote springs to mind.
The overall preoccupations of the electorate do tend to be better reflected with a PR system, especially a STV system that is not mitigated by a representational threshold as in Germany, so any left/right polarisation may well result in representation of those views in parliament, but in the absence of L/R polarisation other factors can come into play. There are downsides to both full representation of the plurality of opinion in any given constituency, and lack of representation of diversity of opinion. The Weimar experience casts a long shadow over Germany, whose constitution errs on the side of caution.
PR can result in election of independents who are very popular in their own constituencies for reasons including personal popularity, but bringing tangible benefits to constituents results in long term re-election. Independents can end up holding considerable power if larger parties are neck and neck. This has been the case in Ireland.
www.irishtimes.com/news/independent-td-tony-gregory-dies-at-the-age-of-61-1.833692
The fact that representation is proportional to the vote in any given constituency in Ireland means that the ballot box has an appeal for groups which might otherwise retain full trust in the armalite and eschew engagement in the political process. The give and take of parliamentary life, engagement with the media, and the necessity of engaging with the voters tend to have an effect on groups dipping their toes in the electoral process. This is how the (fascist) Blueshirts ended up merging successfully into Fine Gael, and the Republicans who fought a war of independence and a civil war ended up dominating Irish electoral politics for decades in the form of Fianna Fail. We now see Sinn Fein being moulded by engagement with the process and attention to the way of thinking that it necessitates.
Majoritarian electoral systems are not necessarily representative, as pointed out by John Stuart Mill.
In a representative body actually deliberating, the minority must of course be overruled; and in an equal democracy, the majority of the people, through their representatives, will outvote and prevail over the minority and their representatives. But does it follow that the minority should have no representatives at all? ...Is it necessary that the minority should not even be heard? Nothing but habit and old association can reconcile any reasonable being to the needless injustice. In a really equal democracy, every or any section would be represented, not disproportionately, but proportionately. A majority of the electors would always have a majority of the representatives, but a minority of the electors would always have a minority of the representatives. Man for man, they would be as fully represented as the majority. Unless they are, there is not equal government ... there is a part whose fair and equal share of influence in the representation is withheld from them, contrary to all just government, but, above all, contrary to the principle of democracy, which professes equality as its very root and foundation.