When searching, look who underwrites the insurance they sell (e.g. Huddle is underwritten by Holland Group of South Africa). Then look into the financial/annual reports of the insurer and underwriters to see where their interests lie and who their investors/shareholders/funders are. It is also worth doing searches on the investors to see what they also invest in (as they often invest in things other than the company in question).
These can be done using google searches and looking at financial information posted on the company websites. There are also investment media articles and company announcements particularly where companies are public (listed) companies.
There unfortunately is not one site but many but the above will get you on your way to find out relevant information.
The reason why I am always skeptical about such claims is that it is highly probable that the capital investments from shareholders uses money from the same shareholder’s investment in the same industries which the parent company claims are unethical.
Since the start of the industrial revolution, the fossil fuel (and mining) industry has resulted in a significant proportion of the wealth in the world either from its exploitation or the profits being used to invest in other industries.
If a company was ethical in the pure sense, they would refuse investment from anyone who has gained wealth from the same industries the parent company is avoiding due to its ethical investment rules and potential ethical conflicts. Not doing so just means that the companies claims are potentially making misleading claims.
Using Bendigo Bank as an example since you have listed it above (and assuming that it was a 100% ethical bank…which is not the case as it only potentially meets this for some of its investment funds). It is a publicly listed company and many of its major shareholder are well known (refer to the annual reports). Take their no. 1 major shareholder HSBC Custody Nominees (Australia) Limited, which is a fully owned subsidiary of HBBC bank. It’s no. 1 shareholder historically has investments in/with the fossil fuel industry (see its annual reports) and has gained much wealth from these investments. While insuring with Bendigo Bank’s because they have some ethical investment funds may be admirable, in effect its major shareholder invests in companies that their ethical investment funds may avoid.