I would like to know how proponents of non-sexist writing suggest you
refer to the pronoun associated with ships and boats. Is "she" still
acceptable?

How about "it"? Boats don't have a gender, after all!

Grammatical gender is not "sexist". Some languages have grammatical
gender for all articles, which doesn't make it "sexist".

In any case, "it" could be probably acceptable.

yes, generally all the non living things are refered as "she"   
for ex: world ,countries

 so definitely boats/ships can be callled as" she"

Definitely "it".

@daredevilmohan-ga 
- Der Vaterland, das Reich ?

@lynnes-ga
- I strongly suspect that anything other than 'she' is highly unacceptable

WHY IS A SHIP CALLED "SHE"

A ship is called 'she' because there is always a great deal of
'bustle' around her.;
There is usually a gang of men about;
She has a 'waist' and 'stays';
It takes a lot of paint to keep her looking good;
It is not the initial expense that 'breaks' you, it is the 'upkeep';
She can be all 'decked' out;
It takes an experienced man to handle 'her' correctly;
And without a man at the helm, she is absolutely uncontrollable;
She shows her 'topsides';
Hides her 'bottom';
And, when coming into port, 
ALWAYS HEADS FOR THE 'BUOYS'.

That is why a ship is called "SHE"