First, let me say two things that writers/producers/directors seem not to understand:
#1 - People do not watch television to have moral lessons shoved down their throats. They watch television to be entertained. Moral lessons are (typically) not entertaining.
#2 - Never, ever trade good writing for special effects. You will always end up in the red. Nobody cares if there's a superbly-crafted monster shown on the screen if the plot doesn't make sense.
Now, let me cover why (in addition to these two points), why this season went horribly, horribly wrong.
First, let me say that it isn't a problem that Dr. Who is female. Or, rather, it didn't HAVE to be a problem. The writers (and wardrobe department) made it one by not dealing with that shift properly.
1. WARDROBE Dr. Who is an absent-minded, eccentric genius. The suits that previous incarnations of Dr. Who would wear would give him an air of respectability while he was making a fool of himself on his way to ingeniously solving some complex problem. This incarnation of Dr. Who looks like she stole the clothing of a gender-fluid toddler. It doesn't give her any air of respectability, so she ends up looking ditzy, crazy, or ridiculous. The very obviously bleached hair doesn't help because it goes against Dr. Who's very long history of not caring much about appearances (and when Dr. Who has cared, the fashion choices were more geeky/dorky, not superficial).
2. PREACH, PREACH, PREACH I watched years worth of Dr. Who and never - EVER - have there been so many moral lessons shoved in my face. Typically, there is a good balance of: (a) random adventures, (b) the occasional horror episode, (c) races that were interacted with in the past come to continue the story line, (d) an old acquaintance of Dr. Who asking for help (so we get to learn a bit more about Dr. Who, who is a bit of a mystery), and (e) some well-crafted moral lesson. This season is completely imbalanced. Every episode is some social justice lesson and it's not entertaining. Beyond the irritating condescension, it is incredibly presumptuous. Even if I did manage to make it to my age without any knowledge of morals, quite possibly the last place I'd look to educate myself on how to be a moral person would be television. Not only isn't television a trustworthy source, it's also not the point of television: ENTERTAINMENT is. If I were watching Mr. Rogers or Sesame Street, that would be one thing. But, this is Dr. Who. Come on!
3. POOR EXECUTION Dr. Who doesn't like guns. This is established. Dr. Who gets ANGRY when people are killed. This anger is driven by empathy, but also by having seen too many people die and being fed up with it. Having this Dr. Who play that anger off as mopey (as in the witch-related episode) is weak and pathetic and shows no conviction. This is very out of character. I realize that anger can be harder for a female character to play without seeming hawkish, but deal with it. This is Dr. Who's established personality. You can't just change who Dr. Who is as a character. This is something that even stayed the same through previous male incarnations, so biological differences didn't make a difference. You need to keep the continuity. Write it better, act it better.
4. TOO MANY PEOPLE Another huge mistake was adding so many sidekicks. Imagine the episode duration as a pie. More people? Smaller slices. BAD plan. We're hungry. We want a generous slice of Dr. Who - not fifteen or fewer minutes, with the rest of the time dedicated to humans and their personal problems. Dr. Who is a Time Lord. We're still unfolding all of what that means and trying to learn more about Dr. Who's past. There are so many species out there, so many unexplored worlds. But, here you are filling up our time with the problems of a few human characters. If we wanted that, we could've watched another show! ANY other show. The point of this one is to see all of time and space - which (believe it or not), does not revolve around a few humans.
5. IDENTITY CRISIS (!?) The whole "I don't know myself," "I'm lost," bit was taken way, way too far. Yes, we get it, it's disorienting being reconstructed from scratch in a new body and having to reorder hundreds of years worth of memories. But, having a female Dr. Who in the midst of an identity crisis is more the plot for a Lifetime movie than an action/adventure sci-fi series. It makes Dr. Who seem neurotic. This incarnation could've been made a bit more serious to compensate for the difference in sex stereotypes and norms. That would've kept Dr. Who's personality and personal strength more intact. But, as is, it's a mess. You turned Dr. Who female and didn't do enough to compensate for it and now female Dr. Who seems weak, pathetic, mopey, and ditzy. What a total disappointment! (And, I say that as a woman, myself.) It didn't have to be this way.
6. BAD WRITING The writing for this season (11th) is absolutely horrendous. Have any of these writers ever actually watched Dr. Who? Do they know what the word "continuity" means? How about "character" or "established personality"? It doesn't seem like it. It seems like you recruited people on to write for this show who didn't give a toss about the personality of Dr. Who, the continuity of that character, and the balance of themes that previously existed in the series. Get people working for this series that actually care about keeping it as good as it WAS (I say "was" because this season is the worst I've ever seen). Not only is the character of Dr. Who being slowly dismantled over the course of this season, the overarching themes are imbalanced, and nothing about this series which drew me to it to begin with has been left intact. Find a crazy, obsessed fan that can recite lines from various episodes by heart. Then, hire this person as a consultant (they'd probably work for free just to be part of the production, so you might not even have to pay them). Make sure you actually LISTEN to this person when it comes to wardrobe, character, and plot lines. If you did that, maybe you'd actually have a chance of recovering from this train wreck of a season. To be clear, it's not bad because Dr. Who is female. It's bad because your writers don't know what they're doing and your lead actress is either not being properly instructed on how to play off certain personality traits (see the previous note about anger over people getting killed) or she doesn't have the acting ability. Either way, this isn't a problem with Dr. Who's sex. It's a problem with other people not doing their jobs sufficiently. Please fix it, otherwise you will not only have ruined an incredible series, but you will have ruined it with a woman (which, given your seeming obsession with moral lessons, would probably be a big no-no).