I found Twitter to be pretty civil in its response to the death of Biden’s dog, within the narrow timeframe between it being announced and that tweet. I found more examples of people claiming Republicans were mocking Biden about this than I did Republicans (or people one could assume are Republican) doing anything that could be construed as mocking Biden or the dog's death or similar.
On Twitter, you can search
(dog OR champ) biden min_faves:1000 since:2021-06-18 until:2021-06-20 to get many Tweets talking about the event around the time that Takei tweeted. I scanned through the "top" results, and found this:
- 19 consoling or neutral/factual Tweets
- 1 joke Tweet. It does not seem politically motivated as the account mainly jokes about death.
- A Tweet mocking Rush Limbaugh (but not the dog), quoting a screenshot of a deleted Tweet from an account that I can't quite identify politically except as anti-MAGA.
- Another joke. I don't think this one is mocking the death of the dog, but I would certainly interpret some of the responses to it as doing so (though none have many likes)
- A joke about a drawing of who the dog would meet in heaven (doesn't seem to be hostile to me though)
- I saw Takei's Tweet in this search, and I saw another (27.5k likes) talking about the same thing, and another that may hint at this
Other than these, one message stood out to me, the Tweet written by National Review writer Dan McLaughlin (@baseballcrank):
Champ Biden dies, Major lives on. The Biden family tragedy in miniature.
The reactions to this Tweet make it clear that many people saw this as blatantly offensive, a dismissive, mocking response. For example, "You are a truly awful person" and "This is beyond horrid. Delete this & apologize." Many people left even stronger negative reactions to the Tweet. A link to this Tweet can be found in the replies to Takei's. It seems to me like this may be what Takei was referring to in his tweet.
You can find other popular Tweets mocking the death of the dog (example from a political "satire" account), though they do not have as many likes nor have they been from notable people.
When I looked at news articles via Google News using a similar search, I found even less of note. There were a handful of articles that were consoling or neutral about the dog's death, and really only one noteworthy article beyond that: McLaughlin's National Review article. It mentions the dog dying in passing (not mocking that), then goes on to criticize the Biden family for unrelated things (comes off as a bizarre and perhaps inappropriate transition from the beginning of the article). However, we can say definitively this is not what Takei was talking about, as it was published after the tweet.