You are right that my suggestion does not work, it caused sales order entry to completely fail.
The problem is not just limited to tax exempt suppliers. STRICT_ALL_TABLES for also caused sales order entry for an order with a tax exempt item to fail as well:
Cannot save trans tax details
error code : 1366
error message : Incorrect integer value: '' for column 'tax_type_id' at row 1
sql that failed was : INSERT INTO 1_trans_tax_details (trans_type, trans_no, tran_date, tax_type_id, rate, ex_rate, included_in_price, net_amount, amount, memo, reg_type) VALUES ('13','6083','2019-01-24','','','1',1,'3.15','0','auto',NULL)
The sql failure is the same as the tax exempt supplier problem:
DATABASE ERROR : Cannot save trans tax details
error code : 1366
error message : Incorrect integer value: '' for column 'tax_type_id' at row 1
sql that failed was : INSERT INTO 0_trans_tax_details (trans_type, trans_no, tran_date, tax_type_id, rate, ex_rate, included_in_price, net_amount, amount, memo, reg_type) VALUES ('20','5','2018-12-31','','','1',0,'10','0','rr8','1')
On my site, these errors are easy to reproduce. On the demo database, I changed DinoSaurius to Tax Exempt. Then I tried to create a direct supplier invoice with a single item.