Which is more natural?
The easiest thing to do is to call for a taxi
The easiest thing to do is call for a taxi
And what do you call this to in grammar terms if any?
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They're both acceptable. Searching the Corpus of Contemporary American English (COCA), I find:
thing to do is to [V*] 208 results thing to do is [V*] 93 results
I find similar results searching the British National Corpus (BNC):
thing to do is to [V*] 67 results thing to do is [V*] 18 results
As you can see, we find plenty of examples both with and without to, but the version with to is somewhat more common in both American and British English. In both versions, the complement of be is an infinitival clause, so the verb appears in its plain form (call in your example).
In this context, to is an infinitive marker. It's usually required in this sort of sentence:
1a. What I want is [to call for a taxi].
1b. *What I want is [call for a taxi]. ← ungrammatical
But if the subject noun phrase contains a subordinate clause with do, as in your example, it's optional:
2a. The thing to do is [to call for a taxi].
2b. The thing to do is [call for a taxi].
Both are grammatical, and there's no difference in meaning. The version with to seems to be a bit more common
By the way, in The Cambridge Grammar of the English Language on p.1255, Rodney Huddleston gives the rule as follows:
The bare infinitival is restricted to cases where the subject NP contains do in a relative clause[.]
But this rule doesn't seem to be quite right because to is optional in your example as well, as we can see from the corpus evidence above, so in this answer I've tweaked the rule to use the more general term "subordinate clause" rather than "relative clause".
For the moment, I believe this is more accurate, but you can do further research if you'd like to try to nail it down.
In the searches shown above,
[V*] is a part-of-speech tag representing "any verb". You'll have to scroll down on the results pages if you want to see the totals. If you'd like to see actual examples of usage, click some of the matching phrases; the examples will appear in the bottom right.
In this answer, the * symbol marks an utterance as ungrammatical in Standard English.
I've encountered this problem twice:
Wikipedia cited a quote by Stephen Hawking that All one can do is find which mathematical models describe the universe we live in.
Prof. Anne Aly in a Q&A TV show used the same pattern: The first thing that they do with their propaganda is tell young people to reject their Australia citizenship, to reject their Australia identity.
I thought it's acceptable but sounds like a misspoken, and ungrammatical.