Nothingness, in phonetics, shouldn't be represented with Ø (Capital Letter O With Stroke), it should be represented with ∅ (Empty Set). This symbol is bigger and is shaped like a circle rather than like a letter O (which is squished horizontally in most fonts). But, some linguists made do with Ø back before ∅ had widespread font support.
Either way, though, phonologists generally don't seem to have an issue distinguishing capital from lowercase letters. Lowercase c is the IPA symbol for a voiceless palatal stop, while capital C is frequently used to mean "any consonant", and this hasn't caused too many problems.
(Though anecdotally, I did once cause a lot of frustration for myself when I used *o and *O for different reconstructed phonemes in a lecture. No issue on the slides, but trying to keep them distinct on the chalkboard was a nightmare!)
If it becomes an issue when writing about a particular language (say, one where front rounded vowels frequently get deleted), the author can choose a font that emphasizes the differences, or use a different symbol for one or the other: I've seen ö for the vowel and {} for nothingness plenty of times.
The distinction that you refer to comes from mixing two entirely different alphabets, that of formal language theory and that of the IPA. ʃ, ɛ, ɑ, ɣ which are phonetic symbols also resemble mathematical notation. The distinction between ɵ and θ is a more problematic visual distinction, since these are both IPA symbols. The symbols are similar but not identical. A rule changing /a/ to a front rounded mid vowel before [i] is informally written as "a→ø/_i" (the formal rule would involve clearly different feature expressions). A rule deleting /a/ in that context would be written as "a→Ø/_i".
The only real problem is a computer-coding problem, that in Unicode, visually-identical letters can have different codes, depending on what block they are in. Example: Greek ε and IPA ɛ. This isn't a linguistic problem, it's a computer problem.
So in math, I've always been taught to write my zeros with a small slash through them to differentiate between them and the letter O. Also, there's the symbol "∅" which denotes the empty set and is called the 'null sign'. If you are doing math in Norwegian or Danish, how do you avoid confusing the letter ∅ with these symbols?