Final answer:
Option (A), The colonists objected to their ships and homes being searched for taxable items because they believed it violated their rights as Englishmen, insisting on the principle of "no taxation without representation" given they could not elect representatives to Parliament.
Step-by-step explanation:
The primary objection the colonists had when tax collectors searched their ships and homes was that it infringed on their rights as Englishmen. They contended that without the ability to elect representatives to the English Parliament, they should not be subject to direct taxation, upholding the principle of "no taxation without representation". This concept was based on the rights enshrined in the Magna Carta and the English Bill of Rights which declared that people have the right or their representatives must give consent to taxation.
The British Parliament, specifically the House of Commons, imposed these taxes without understanding of this fundamental difference in perspective, assuming virtual representation was sufficient. Taxation was seen as acceptable for regulatory purposes but not as a means to generate revenue without the colonists' consent. They could not vote for representatives in the House of Commons and felt direct representation was the only legitimate form of governance.