I don't know their methodology, but you can double check their results yourself. If 3600 responses is too much to go through, you can do a random sampling of a smaller set. I've looked at the first 10 submissions from individuals. 8 of them are opposed to the law, 1 is unintelligible, and one thinks the law, as proposed, doesn't go far enough.
Alternately, you can try to find reports on this consultation from some media that you trust. Though you may find they are all silent on it.
The only source for the "vast majority of respondents expressed opposition" claim I can find is your quoted source, a site that seems to focuses exclusively on culture war topics, and is based on their own analysis without publishing their data. Not a reliable source. I took a look at the gov.ie link you shared. It seems there were 104 written individual submissions, and 3528 online individual submissions. Whatever the prevailing mood of the responses, can this be taken to be an accurate snapshot of the public mood of a nation of 5 million people? Also, the gript.ie analysis ignored submissions by groups and elected officials.
Or is the photo of a page of that law, showing that possession of material likely to incite violence or hatred (with no mention of truthfulness as defense) falsified?
This law was debated in the Dáil by the TDs elected by the people to represent their views. People raised issued, amendments were made. The issue around possession of material likely to incite violence or hatred was raised. There was a largely civil public debate around it, where various groups raised various issues, including the specific one you mention. It just didn't go your way. This is how democracy works.
What's happened here is that this seems to have been picked up by the US right (Donald Trump Jr. and Elon Musk have rowed in) and it's brought a lot of attention to it. We largely don't have the deeply polarised discourse here that the US has, our democracy is largely civil and functioning more or less as well as such an imperfect system can. What we're starting to get here in recent years is a vocal and emboldened fringe minority who feel entitled to bring the validity of the whole system of societal decision-making into question when it doesn't support their views. This is the thing that is dangerous here, we've already seen this trend lead to violence in the US.
Please be specific. Is the claim "The Irish government is proceeding with legislation to outlaw so-called “hate speech” – even after the vast majority of respondents to their public consultation expressed opposition to the idea" [1] false?
Or is the photo of a page of that law, showing that possession of material likely to incite violence or hatred (with no mention of truthfulness as defense) falsified?
I understand some claims in that thread are speculative, but the majority is factual. Feel free to dispute the speculation, but please don't use it to trick people into thinking you've also disproven the facts the speculation is based on.
[1] https://gript.ie/hate-speech-consultation-received-mostly-ne...