As this NGram shows...
...the construction [verb] on regardless is commonly used with a variety of verbs such as carry, press, go push, pass, for the (metaphoric or literal) sense of continue a current action or direction of movement [disregarding/ignoring any pressure to stop or change course].
As has been pointed out, there's nothing inherently wrong with "redundancy" in English (it's often used quite naturally to convey emphasis, for example). But noting in particular the significant increase for to carry on above, I'm inclined to say that specific combination has become something of a "fixed expression" in recent decades.
Precisely because it's become so common, the exact meaning of to carry on regardless has become somewhat vague in the minds of many speakers. Sometimes it just conveys a general sense of continuing to do something diligently, industriously, laboriously, purposefully, resolutely, with no particular allusion to in spite of [something that might stop the activity continuing].
Consequently, many native speakers wouldn't even notice the "repetition" in OP's example.