The only way in which BlueSky is preferentially catering to the left is by existing as an alternative to X and specifically providing tighter control of what is in your feed; and this is only “catering to the Left” because of the groups towards which X either has weakened or stopped enforcing its policies against harassment towards.

(In a market with strong network externalities, being the dominant player is self reinforcing and it takes failing hard to lose that positions, and its naturally hard to compete because getting users is a chicken and egg problem.)