Left and right are political terms indicating whether one leans towards communism or its cousin socialism or whether one leans towards the law of supply and demand (the market) and accepting personal responsibility for the situations one finds oneself in rather than foisting one's troubles upon everyone else.
Left and right in Catholicism is perceived especially and perhaps uniquely in the US as attached to political affiliation.
Catholics ought not to be primarily concerned with politics but with the morality of the decisions which politicians arrive at. If those decisions of whatever 'party' conflict with Catholic doctrine, then the Church dutifully opposes them. This does not identify the Church as a supporter of a political party but as witnesses to the Truth.
To me, an observer from outside, it seems that 'progressive' Catholics in the main align themselves with the Democrats regardless of the anti-Catholicism of the Democrat's agenda.