TL; DR: Yes.
I grew up in Malaysia and I am a non-Muslim.
I have been inside Putra Mosque, in the capital city of Putrajaya.
It was part of a class field trip I had when I was in school.
However, you should pay close attention to etiquette and expected behaviors as outlined in your own answer.
The girls in my group wore long sleeves, and shawls to cover their hair.
travel.stackexchange.com/users/65923/casvaart
Yes, non-Muslims are allowed to enter (at least some) mosques in Malaysia.
See user casvaart's answer for a local's perspective.
travel.stackexchange.com/users/36332/Urbana
Having been in Malaysia, I can attest that visiting a mosque is possible for non-Muslims.
There were no restrictions as far
I could tell
and I have entered at least a dozen mosques principally around Kuala Lumpur
but also some in southern provinces.
In some cases, there were signs indicating not to take photos within the prayer hall itself but the outer part of the mosque can be photographed.
travel.stackexchange.com/users/4801/Itai
Generally yes, but you might be asked to wear appropriate clothing (e.g. no exposed skin).
But even then you might be given a gown to cover yourself with during your visit.
At least that was the case at Putra Mosque (seen here )
travel.stackexchange.com/users/12426/Nobilis
I can't speak for every mosque in the country but certainly from my experience of visiting a few mosques in KL and Malacca
it's a case of "Sort of".
The mosques all had visitor areas where nobody had any issue with me, a white guy in jeans and a plain t-shirt coming for a look around.
Signs said no shorts and no shirts with pictures of skulls (or other wild things) on them
but I encountered zero issue, they're used to tourists.
However...this was only to see a visitor area.
To go into the main part of the mosque itself where the worship takes place; the big two in KL had signs explicitly saying this was not allowed for non-muslims.
If I remember right the national mosque had set hours when non-muslims were allowed to take tours but generally it wasn't allowed.
travel.stackexchange.com/users/33257/the other one
When I was in Morocco, I was disappointed to find out non-Muslims, in general, aren't permitted in mosques in the country, but I heard this isn't the case in some other countries. I'm headed to Malaysia soon and might want to step inside some mosques when I'm there.  Are non-Muslims permitted to enter mosques in Malaysia?
Are non-Muslims allowed to enter mosques in Malaysia?
travel.stackexchange.com
<legal><malaysia><cultural-awareness><islam><mosques>
travel.stackexchange.com/questions/99278
travel.stackexchange.com/users/36332/Urbana
You are allowed to visit many mosques, but you might be asked to wear appropriate clothing and may not be allowed in certain areas or at certain times. Non-muslims are allowed into mosques in Malaysia to some extent, provided that they wear appropriate atire. Though they are usually kept way from the main worshipping area there are some cases where they can take a tour during certain times. An example of this can be found at the National Mosque in Malaysia. 
Yes there are mosques in Malaysia that allow non-muslims to enter provided they wear appropriate atire. In most cases the main part of the mosque is off limits to non-muslims, howevere there are some instances where non-muslims may take a tour of the main area during certain hours i.e the national mosque in Malaysia