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IMO, whether or not Gwen is canonically transgender is irrelevant, because thematically the two are equivalent. Being spider-woman is allegorical for being transgender.

• She knew she was different before anyone else did
• The way that she's different would affect how others see her once they find out, very possibly putting her in danger, depending on who finds out and how hateful/vengeful they are.
• She could theoretically quash that part of herself and live the way everyone expects her to, but to do so would be to kill a piece of who she is
• She had to "Come out" to her dad (and not by choice, really. She only did so because she was caught with her new clothes.)
• She wasn't accepted for who she was in that coming out, but knew it would be easier to live without her closest family member's support than to live without being herself.
• She found a community of others like her, who all have unique but similar experiences and who are eager to support one another.

The colors may be an indication that Gwen specifically is trans, or a hint to the audience that to be a Spider-person is an allegory for being trans. Her character was designed with the white, pink, and blue color scheme in 2014, so it's not all that unlikely that the color scheme was an allusion to the trans pride flag on purpose. Maybe a writer or character designer clarified somewhere exactly how intentional or coincidental this Spider-Gwen/Transgender connection is, would be cool to see if so.

At the end of the day, the story serves to make people more empathetic to others who have to weigh their identity against their safety, especially in cases where the facet of their identity in question could be intentionally kept hidden.