What to do when a reviewer is late while daily posting about other activities on social media?
You have to separate two things.
First, it seems your journal has certain procedures regarding late reviews. You say that "if [you] do not receive a reply, [you] cannot grant the extension". You have not received the reply, so simply do not grant the extension. Do whatever you do whenever you do not grant an extension; I assume that this means telling the reviewer that they are relieved of their commitment to review the paper due to being 40 days late and not replying to reminders, as well as finding a new reviewer and probably notifying the author(s). What you saw on Twitter is not involved in that.
Second, you have to think about your relationship with this reviewer. Unless you have a very compelling reason to continue asking for the services of this reviewer, then I would consider not asking anymore. Being very late – I assume that 40 days is a long time for a review in your field – is one thing, not answering emails is another, both combined with public posts about spending all their time on non-work related stuff is not great. Unless the tweets are about helping the authorities deal with the outbreak or taking care of vulnerable persons close to them, I understand your frustration. Referees provide a very valuable service for free, but committing to do something, not doing it, and not communicating about it (while being clearly able to) is not okay.
Perhaps this is worth pointing out. I would guess that the tone of the tweets also matters. If it's something like "great, I'm stuck at home so I have an excuse to stop working", I think being annoyed is fair. If it's rather "wow, dealing with confinement is hard, thankfully I have these activities to take my mind off it", I would be a bit more wary. Dealing with the current situations is difficult, and for some even more so. I don't know what country the reviewer is from, but in some places, it has been forbidden by law to go outside your home (except for essential reasons) for weeks/months. This takes a toll on the mind. It can cause emotional trauma, even PTSD or depression, according to experts. Keep that in mind before cutting off the reviewer.
recently I noticed on my Twitter feed a number of their posts (retweeted by people I follow) about how they are using the lockdown to do a lot of non-academic stuff, which is fine but I feel it no longer justifies using the lockdown as an excuse for being late.
You can't control the reviewer's personal life, nor should you be prying into the details of what they do with their time. Mentioning this at all would be extremely unprofessional. And if you don't mention it, you are going to need to come up with a different reason when you email them. So just follow the normal process and ask for an update on the review, or say we need it by X time.
it is inappropriate to use such a difficult situation to justify being late, while actually doing something else.
This is completely an assumption on your part, there is no proof that this is they are doing. No one spends 100% of their free time on work. So you are saying if I'm having a hard time due to the pandemic, then I'm not allowed to write non-work related posts on Twitter?
Your reaction to their posting on Twitter is inappropriate; you don't know their situation. In the worst case, perhaps despite whatever they are posting on twitter, their parents are dying of coronavirus and they are taking a break. You don't own their time.
I'm not sure that you need any "grounds" for un-inviting a reviewer at all.
But I would, myself, take another tack first. Ask them when you can expect the review, reminding them of its importance to the journal and the author.
Ask if there are any specific reasons why the review is over a month late.
If the response you get is unsatisfactory, ask them if they are really still interested in reviewing for this journal in the future or not.
Perhaps you will learn something important and perhaps your decision will be clearer/easier after hearing any response.
But, in the meanwhile, I'd prepare to send the review to someone else.