Is it okay to start a sentence with a variable? Do I need to rewrite a sentence just because the subject is typeset as a Greek letter?
Φ is treated in a special way.
The variable Φ is treated in a special way.
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In more scientific/mathematical writings it may be more acceptable to start a sentence with a symbol, if only because of their higher profusion in texts and because the need for such constructions is frequent enough that rephrasing all of them may make a text a lot clunkier.
In particular, I note that the Physical Review Style and Notation Guide recommends (§III.A.1) only that authors
(2) Avoid beginning a sentence with a symbol if the sentence before it has ended with a symbol or number.
There is no discouragement on authors beginning a sentence with a symbol, though.
Similarly, the IOP Style Guide (Numbers, p. 13) discourages the use of numbers at the start of a sentence, but doesn't say anything about symbols. In discussing the use of symbols within text, the AMS A manual for authors of mathematical papers is markedly divided on this issue:
Some writers do not hesitate to begin a sentence with a mathematical symbol, but others regard this as a barbarism.
On the other hand, the British manual Journals of the London Mathematical Society: house style and instructions for copy-editors and typesetters is quite decisive in the negative (§7.1(g)):
Sentences should begin with words rather than symbols. Phrases such as ‘It follows that’, ‘Since’, ‘We have’, ‘We see that’, ‘We ﬁnd that’, ‘Now’ and ‘The function’ can be inserted to avoid sentences starting with maths and to avoid formulae being separated only by a comma
Within the mathematics and physics communities, I think the general gist, then, is to try and avoid constructions like that, but to use them, sparingly, if your text would otherwise accumulate too much clutter.
That said, I tend to find that whenever I am in that situation, there are usually alternative phrasings that don't start with a symbol (Greek or otherwise), and these phrasings tend to be clearer and easier to read. In such cases, it is easy to get "scoped in" and get the impression that there's no alternative, but it helps to step back and look at restructuring the sentence or even the entire paragraph, and the restructuring will then make the entire paragraph easier to read.
Also, if you are writing a technical or scientific text, you should consider what proportion of your audience you expect to be non-native speakers of English. Keep in mind that complex, non-standard constructions (like those involving mathematical symbols at the start of a sentence) will be significantly harder on those whose use of English is more limited.
It's grammatical to start a sentence with a variable but the latter variant, "The variable Φ is treated in a special way", is less confusing in the following ways:
Also, the latter variant is advised against by the Chicago Manual of Style in this FAQ entry.
There is one thing that speaks for the former variant, "Φ is treated in a special way", and that is that it's less redundant given that you've explicitly stated that Φ is a variable so that it's obvious to the reader.
If you favor the former variant but want to avoid its deficiencies you might want to consider to incorporate it as a subordinate clause in an appropriate sentence, e.g. the sentence before it.
Think carefully whether or not the latter variant is redundant. If it's clearly redundant you might want to avoid it because being overly explicit can confuse or irritate the reader as much as not being explicit enough.