Will that baby, on Tuesday, when I'm in my Tuesday-blue-T-shirt, regard me as a person? Will he regard someone else, had they being wearing a red T-shirt? Will he be able to separate the idea red from the idea person without the prompt "That was the same person in a blue T-shirt"?

I’m actually relatively uncertain what the answer here is. Definitely babies recognize their mother, maybe from smell or feel and not sight. And your smell would change little, so maybe it does recognize you?

Babies also differentially look at faces, so it seems likely it has an inductive bias to chunk the world into faces. If so, also likely it recognizes you, if it can see you. Because it won’t be looking at your shirt.

Edit: A paper I have not read that seems relevant, and a quote from whattoexpect.com:

• At birth: Even though your baby doesn’t recognize you, she certainly likes the look of you. Studies have shown that even newborns, with their eyesight limited to about 12 inches, prefer to look at familiar faces — especially yours.
• Months 2 to 4: Your baby will start to recognize her primary caregivers' faces, and by the 4-month mark, she'll recognize familiar faces and objects from a distance. She’ll love looking in the mirror, too — but since she isn’t able to recognize herself yet, it’s a social activity: “Wouldn't you know it, that kid keeps showing up at the same place I do!” At this stage, engaging with the face staring back at her is all about fun.
• Month 6: Now halfway through her first year, your baby knows familiar faces and understands if someone is a stranger.
• Month 9: By this age, your baby will likely have favorite toys and objects and will be able to recognize and look for them even when partially hidden: "That's my bear peeking out from under that blanket!"
• Months 15 to 18: Self-recognition doesn't develop for most children until between ages 1 and 1 1/2. So even though your child will recognize many other familiar objects and people halfway through her first year, it takes quite a bit longer for her to look at an image of herself and think, "Hey, that's me!" As toddlers gain independence — walking and talking — they discover themselves as a distinct member of the family.