Evangelicals focus of spreading the news of Jesus and it is their goal to convert non-believers, or people of different religions, to Christianity. They want you to ‘take on’ their beliefs. In this context it means to accept their religion or to adopt their ways. I think this isn’t a very common way to see ‘take on’ used (or at least I dont see it used that way much). More commonly you would see it like: “Whats your take on The Kardashians” If someone says “Whats your take on….” they are asking for your opinion, your ‘take’.

Here “take on” means agree with or accept. Like a lot of phrasal verbs it has different meanings.

To adopt these beliefs, meaning ‘evangelical’ want to convince others to believe as they do Typically, an Evangelical or an Evangelist is a type of American Christian. I’ve never seen it used in any other context.

GuideDogSaint’s answer is correct. I don’t think ‘take on’ is the most natural here. Better would be ‘adopt’ Sentences where it has a similar meaning, similar to ‘accept’ I’ll take on the task of He took on the role of cheerleader for the project. Saying you ‘accept’ a belief is a little weak imo, but not exactly wrong. More common would be to say adopt/hold/share etc.

I will take on a big challenge in answering this question 😂