It's tough, in 2017, accepting that The Talons of Weng Chiang is considered one of the best Fourth Doctor adventures made. Objectively, it has a lot going for it. Great writing, great acting, thrilling pacing, and lovely atmospheric setting. But the heavy racism is something it struggles to come out from under, and in today's age actors in yellowface, or such grotesque charicatures like the puppet, are too uncomfortable to just dismiss as “well it's just fiction.” I still recommend to check it out, and I'm sure there are plenty who won't be bothered by it, but be warned: it can make some viewers quite uncomfortable.
