While clearly intended for closer to the 8-12 range (though I've seen both preschoolers and adults watch & enjoy it) rather than the 'toddler' like you asked for, I still have to put in a good word for Steven Universe. I have not seen a children's show which I felt did a better job of showing positive, yet complex and non-stereotypical, role models and messages in regards to gender, race, and LGBT issues. It also tackled a large number of other complex, but important, topics usually considered beyond the realm of a children's show. It's the sort of show I'd encourage you to keep in mind once your kid is of appropriate age to introduce them to if your looking for better handling of these topics.
The show starts out looking like your standard Monster of the Week style show, which standard action & combat, but near the end of the first season the show starts to grow it's world more and starts tackling some far more complex topics.
The basic premise is that the 'Crystal Gems' have made it their mission to defending earth/humanity. These Gems don't actually have a sex, as they don't reproduce sexually; however, all gems use female pronouns. The gems all have complex personalities that are in no way limited by standard gender roles, they also fall in love and the importance of relationships, how one expresses them, The importance of honesty & consent within a relationship, even the harm of abusive relationships are all addressed in the show, in a kid friendly manner. Thus the reason some jokingly refer to it as "that show about lesbian space rocks."
The main character is male, but one who is very in touch with his feminine side, being very emotional and the Heart of the team, with all his powers focused on defensive and healing abilities that are usually given to female characters. I feel he is both a strong male role model while also shows one does not need to be constrained to standard gender roles to be a strong character.
I also have no complaints with the handling of race. While the main character is white his best friend, and an important and strong character who is definitely not just a side kick, is African American. The Gems aren't human and come in all colors, with one being distinctly African American in coloration. The Crystal Gems' leader, and most down to earth and stable, may be red in coloration, but her body design "is a stereotype, a 'trademark' of Black women’s bodies". Full disclosure since I couldn't figure out how to describe Garnet body design well I did a quick google search for a good phrase and stole the one I found in this article on how Steven Universe handles race well.
Race and racial issues are tackled by allegory also. The type of gemstone each gem possesses works as a surrogate for race in this case, with their tackling issues such as some gems being used as little more then servants/slaves for important gems, and the struggle to not be identified exclusively by one's gem.
In terms of LGBT representation the relationships held by 'female' gems is the most obvious area that can be discussed. However, one 'character' that comes up later is explicitly depicted as unclear gender, seen as pretty by both sexes, and is presumably non-gender binary.
In addition to everything above the show also touches on a number of fairly deep topics, sometimes sometimes by allegory, in a manner that can be understood by children. A small list of these topics include:
- The struggle of trying to live up to some high standard you, or others, set for yourself, and the feelings of inadequacy failing to live up to those standards can bring. In fact the majority of characters struggle with this in one form or another.
- That an Idol may not be perfect, and that you can continue to care about someone, even if they don't live up to your idealized vision.
- Sense of abandonment from not knowing a parent and the desire to know more about them.
- Sense of failure and how to keep moving on despite one's mistakes
- PTSD and the difficulty of moving on from a painful experience or memory
- The importance of compassion and empathy and willingness to try to forgive, but also...
- Realistically depicting that some will not be easily redeemed by ones compassion, unlike what many kids shows would do, which also leads to...
- The struggle of being forced to make difficult decisions and regret of not being able to find better solutions.
This is the one show I most want children to watch, because I feel that it covers a huge number of positive messages; and particular addresses messages and topics children are rarely exposed to in children's media but still can benefit from seeing them depicted. I would definitely encourage you to try introducing your child to check it out when they are old enough,