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I consider this a very smart move and reminded me of the many situations in which the Apostle Paul found himself in the New Testament, both in the Book of Acts and in his later ministry, as summarized in the following verses which he wrote under God's inspiration (I Corinthians 9:18-23). Verses 20b-22 speak directly to this incident.

18 What is my reward then? Verily that, when I preach the gospel, I may make the gospel of Christ without charge, that I abuse not my power in the gospel.
19 For though I be free from all men, yet have I made myself servant unto all, that I might gain the more.
20 And unto the Jews I became as a Jew, that I might gain the Jews; to them that are under the law, as under the law, that I might gain them that are under the law;
21 To them that are without law, as without law, (being not without law to God, but under the law to Christ,) that I might gain them that are without law.
22 To the weak became I as weak, that I might gain the weak: I am made all things to all men, that I might by all means save some.
23 And this I do for the gospel's sake, that I might be partaker thereof with you.

There is also an Old Testament record where God's prophet okayed a believer going into a pagan temple with his employer (the King). While outward observance and show is all important to many non-Christian religions (wash feet, face East, etc.), the true God looks on the heart of a man.