That would be bad if baby Yoda was there solely because he was a marketing gimmick. He is integral to the entire story and will seemingly be important in season 2 as well. Also remember that toys were not announced until after the series premiered. If it were only to sell toys, this would not have happened. We’re talking about Disney here, the company who showed BB-8 and porgs months before their films release to sell toys.
Yes, he could be considered a babysitter, but a man taking a child under his wing to protect them is actually a masculine quality found in stories and cinema. The Last Of Us is a relevant modern example right now. Is Joel lees masculine because he took Ellie and protected her from people who wanted to experiment on her? Same applies here. He is in no way acting like a woman when he is around baby Yoda. I think any father would feel the same way, probably why Jeremy hasn’t said anything about it.