Is "itbabagoods.com" safe?

Just by the name alone it sounds shady.

If ever in doubt try googling storename reviews.

No, it is more than likely a scam, since I didn't see any legal information, like where they have registered or where to contact them outside the web. Also, trust-wise from a usability viewpoint that site is terrible. For example: They have socal media icons, but they are not link to account. Even if there is a real retailer behind it, I wouldn't trust him, if this is how he opperates his website.