If you're a "centrist" and you only ever repeat right-wing talking points like "the economy" and criticize left-wing policies like social welfare...
Then you're not a centrist, you're just a right-winger who doesn't want the bad reputation associated with it.
@MutualityWSDEs Generally speaking, "centrism" is some sort of position where one is "critical of both sides". That can take a few different forms, but a lack of alignment with any one "side" is the main characteristic.
(I think this is still a morally bankrupt view to hold, but that's besides the point here.)
If one is always criticizing left-wing policies while parroting right-wing ones and calling them 'neutral', then they're not critical of both sides, and therefore not centrists.
@joepie91
Yes - this makes a lot of sense, particularly in relation to the group you described in that they seldom say anything critical about the other side, only the left which they term 'hard/extreme/far left' perhaps implying they somehow represent healthy leftism in their (actually nonexistent) critique of the right.
In the context of UK establishment electoral part of the left (called 'Labour), they only ever attack the 'far left' and extreme and obviously egregious elements of the right.