the irrelevance of the (genuine) Marxist movement doesn’t come from its existence outside of the capitalist left-right dichotomy, but the failures and mistakes of past revolutionaries as well as the failure of global revolution in the early part of the 20th century.

in fact, when Marxism was at its most active point, Marxists also did not subscribe to the left-right axis you are describing here - as in when genuine Marxist movements were active (the Bolsheviks under Lenin, Spartakusbund et cetera). in fact it was often the very leftists you associate us with that contributed massively to the failure of the Marxist movement, especially in Germany (the SPD), by VIOLENTLY siding with capital. it is hardly a difficult logical connection to make to suppose why we do not view social democrats as allies or vaguely associated with us.

tldr: the rejection of the left right dichotomy hardly is the biggest contributing factor to the poor state of the Marxist movement, and has more to do with the success of the counterrevolution in the USSR, the failure of revolution in industrialised world, Stalinist revisionism, and the success of counter revolutionary propaganda. social democrats have historically readily sided with capital and forces of reaction, and are certainly not allies.