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I view Doctor Who as part of a great tradition of sci-fi that pushes boundaries. Tennant's era was a primetime TV show that featured gay characters (Captain Jack in particular) without treating it like it was a big deal. When at the time it really wasn't that common (particularly in kid-friendly TV).
These attempts overshoot at times, like when Star Trek TNG put male crew members in "skants"[1] but they can always course correct. If you let minor things like that ruin your viewing of the show then that's on you, not them.
[1] https://memory-alpha.fandom.com/wiki/Starfleet_uniform_(2350...
David Tennant was a great Doctor Who. It's definitely still a good show and I'm sure they didn't swap out the entire production cast between those seasons to 'wokify' it.
People have been making the same complaint about Dr Who for at least 40 years, couched in the language of the day. Same with Star Trek.