Travelling to the US as a speaker in a conference [duplicate]

The information you report receiving from CBP is incorrect. The activities that VWP business visitors are allowed are statutorily the same as those allowed under the B-1 visa. This is controlled by 8 USC 1187(a)(1):

The alien is applying for admission during the program as a nonimmigrant visitor (described in section 1101(a)(15)(B) of this title) for a period not exceeding 90 days.

Section 1101(a)(15)(B) is the paragraph that creates the "B" category of visitors, corresponding to B-1 and B-2 visas.

Whether you can receive a speaker fee as a visitor depends largely on who is sponsoring the conference. To qualify, the sponsor must be described in 8 USC 1182(p)(1), as specified at 8 USC 1182(q):

Any alien admitted under section 1101(a)(15)(B) of this title may accept an honorarium payment and associated incidental expenses for a usual academic activity or activities (lasting not longer than 9 days at any single institution), as defined by the Attorney General in consultation with the Secretary of Education, if such payment is offered by an institution or organization described in subsection (p)(1) and is made for services conducted for the benefit of that institution or entity and if the alien has not accepted such payment or expenses from more than 5 institutions or organizations in the previous 6-month period.

8 USC 1182(p)(1), in turn, describes:

an institution of higher education (as defined in section 1001(a) of title 20), or a related or affiliated nonprofit entity; or a nonprofit research organization or a Governmental research organization...

If the institution does not qualify, or if your plans do not comply with the constraints in §1182(q), you cannot use a B visa (or the VWP). In that case, you would need a different category of visa.

Since §1182(q) speaks of "alien[s] admitted under section 1101(a)(15)(B)," that does leave open the question of whether VWP visitors are included, but the federal register notice makes it clear that they are:

Therefore, if an alien is coming to the United States to engage in activities for which he or she may accept honoraria under [section 1182(q)], the alien must seek admission to the United States as a B-1, rather than as a B-2 nonimmigrant. For those eligible to seek admission under the Visa Waiver Program (VWP), the corresponding WB classification (Visa Waiver/Business) is the proper one.

This provision of the law is apparently rarely used and therefore little known. It's therefore unsurprising that CBP gave you incorrect information about it. The Australian author Mem Fox learned about this the hard way.

To answer the question here for other people who might be in a similar position:

I called CBP to inquire about it twice. Both officers said that travelling for a conference under ESTA is OK and also covering of flights and hotels expenses. However, you cannot accept a fee and be seen profiting from it.

If you want to accept a fee you need a B1 visa.