Well everyone is entitled to their own opinion of course. But to respond to your specific examples, first of all I have inquired of some orthodox folks that I know, and was told something I didn't know: usually if you see an orthodox wearing a baseball cap on the street, he's got a yarmulke on underneath. In other words, the baseball cap is either for style or to keep the sun out of his eyes, not as "the" head covering. And for sure, you never see an orthodox Jew wearing a baseball cap in synagogue, do you? Never.
As for your other examples, the yarmulkes with the commemorative bar mitzvah information on the inside is a whole different thing. I don't think that could offend anyone, because nobody sees it. You're not making a statement drawing attention to yourself, and certainly not about something so crass as a sports team symbol.
Even the example of the finger painted yarmulke, made by your friend's daughter, missed my point. Or maybe I didn't make the point very well. I don't think anyone, most importantly God, would be offended by that. While yes, you're right, it is more about "you" than a standard black or white yarmulke, something about that just seems more OK than a Red Sox yarmulke, because it's personal, it's family oriented, it's honoring a connection with your child, all of which are consistent with honor and respect for God and Judaism's values, and with the seriousness of what you're doing and where you are. I guess the difference for me is the crass commercializing of the symbol inherent in the sports teams yarmulkes. It's kind of like you're sitting in synagogue and you look up and see one of those sports yarmulkes, wouldn't you say to yourself, "Man, I can't get away from that stuff even in here?? Even in synagogue?? If not here, where??"
Your friend's finger painted yarmulke is not a commercialization of it, and neither is the Bar Mitzvah info on the inside.
Thanks for all of the responses. We didn't have a chance to attend a service this weekend because my wife was sick and we got too crazy busy with other things, but I will keep your suggestions in mind for a later date.
The collegiate yarmulkes remind me of the many times I've seen an Indian girl in Cameron wearing the full garb covering her entire head and body (sorry, don't know the correct term for this piece of clothing) while at the same time having her face painted blue and white and covered with devil stickers.
Also reminds me of the Crazies chanting "God's on our side" at the Notre Dame fans when we played them many years ago.