Can employer install any software in Macbook to monitor activity?
It depends, but in most cases, yes they can.

If they issued the MacBook to you, it's their property and they have every right to do as they please with their assets.  There's a simple rule - their company, their rules.

If it's your laptop, they can't force you to install anything.  But that said, you have no entitlement to that particular position.  Again -  their company, their rules.


The first case is pretty cut and dry, so let's explore the second a bit more...
Your employment with a company is conditional, you follow their rules and do what they ask and you get to come back tomorrow to earn another paycheck (yeah, it's a little brutal, but that's what it comes down to).  If they have a policy that says your activity will be monitored and you will use a particular VPN (Tunnelblick), you agreed to those conditions.  So yes, even if it's your laptop, when you agree to certain conditions to work there, you've entered into a contract.  Not holding up your end of it, would be a breach of contract on your part.
Now, remember I said &quot;it depends?&quot;
Well, here in the US, there are contractors (also called 1099s because that's the tax document used to report income).  A contractor is not an employee.  There are laws that govern the relationship between what a 1099 contractor and the employer can enter into contractually.  For instance, if you are hired as a 1099 to market the company's new widget that's what you're hired to to do and that's it.

If they provide you with a laptop, well, it's their laptop so their rules apply.
If it's your laptop, they can't manage you like an employee, because you're not.  If however, their marketing database is secured behind a firewall that requires a VPN to access, well, inherently you'll have to install said software because you won't be able to do the job without it.

Can they monitor your activities?  Yes and no.
If you're connected to their VPN, inherently they can monitor everything you do.  However, when not connected, they have no business monitoring you - your laptop, your rules.  Typically when hired as a contractor, the contract will spell out the metrics you must meet (i.e. sales of so many widgets, so many contacts with X number of prospects per day, etc.)  How they record these metrics varies, but they cannot go outside the scope and micromanage your day to meet those metrics.  If they do, you're no longer a contractor, but an employee.  If this is the case, there are legal ramifications.  What are they?  You need to consult an attorney.  I'm not an attorney, and most importantly, I'm not your attorney.