How can my final render look the same as on program monitor on macbook

Fugedaboudit. It isn't possible.

Really.

I work for/with/teach pro colorists ... for pay. Have for years. So I've been through tons of discussions and programs and lessons, and own and have read some of the major tomes, on color in video post. From very technical total geekout to basic.

Remember, no device actually 'sees' color. Not a film camera, not a digital sensor, not any monitor ever created from CRT to any flat panel tech.

These devices only deal in brightness, and use rather amazing and complex processes in both sensor tech and chips and monitor tech and chips to recreate what our eyes and brain 'see' as color. And as every panel, sensor, or chip off the line actually has a slightly different response due to inevitable manufacturing tolerances ... and all companies turning the bits into joined assemblies for cameras or monitors join different bits, and apply different computations in their chips ... you simply cannot match two devices.

As has been demonstrated over and over. Two high-end $20,000 Grade 1 Reference monitors side by side, fed the identical image from an BlackMagic or AJA breakout device (colorists do not grade on GPU outputs!) and with both monitors calibrated by high-end spectros run by experts ... will appear different to the eye. Every time.

Now throw in the major differences between panel types, grades of panel responce within panels, the vastly different bits used by different companies (sometimes even on the same "model" of whatever) to get sensor to recorded data, or data to monitor screen, then ... they all put their own "special sauce" in the computational parts to "enhance the viewing experience" ... then of course the OS typically want to do it's thing, and every video player has it's own "special sauce" ... get the idea?

This is why pro colorists are trained that no one ever, on any screen or device, no matter how delivered (theatrical, broadcast, streaming, DVD/BluRay, web) ... will ever see exactly what you saw on your screen. It simply isn't physically, technically, possible.

Plus many users go mucking into settings and often don't um ... speaking politely ... actually help things. Like setting the Rec.709 mode on their monitor or GPU to work only in "full" mode ... something idiotic like that. Doesn't actually get any more levels of data, as "full" and "legal" are only different computational paths to endode the identical data ... and of course, there's the old colorist's dictum:

"You can't fix gramma's green TV."

So back to your question ... some Macs, those without refernce modes set to HDTV ... will use the gamma 196 for display of Rec.709 video but only in QuickTime Player, Chrome, and Safari. 

Macs with refrernce modes, if set to HDTV, will use the properly specified gamma 2.4 for Rec.709 video display transforms.

So even among Macs, you cannot get the two to match, ever. It isn't possible.

Now nearly every other device will use a display transform of gamma 2.4 whether monitor, tablet/device, or TV. As will all broadcast-specced systems.

You cannot show the same image at two such widely different display transforms and get a closely similar image. That's past the issue of every screen being different.

And no, "the web" is not 2.2 for video display transforms ... that's the still image display. Players tend to all do the gamma 2.4 for Rec.709 video.

Where 2.2 properly comes into video post, is ... unless you are grading in a semi-darkened (not quite blackened) room lighting, the Rec.709 specs suggest grading while using a display transform of gamma 2.2.

So most users probably should use the display gamma of 2.2 while grading. Because that setting should, by the specs, be based on your ambient lighting while working, and not because the work is going to wherever.