I don’t think either need to be avoided. Kids who would mock initials are not going to know what PMS stands for, nor do I think it would even be mocked. And I don’t see a single issue with TPS. You’re definitely overthinking it!
TPS isn’t bad, I didn’t think about toilet paper until you mentioned it. As for PMS, I really think you should avoid it.
I’m a big initial person. I’d actually avoid both unless it’s honor name or really significant to overlook it
-
It’s not uncommon for people to go by JT, AJ, CK, etc for first name, middle initials… in fact at my college our standard email was also our initials… think PMS10@smu.edu
-
There are some professions that you DO use initials for everything… check your medicine bottles- the initials of the checking pharmacist will be on there
So while some don’t pay much attention to initials- there are certain scenarios that come up and I’d just avoid bad initials if possible
TPS definitely does not make me think of toilet paper (other than immediately after you suggested it). As for PMS… I can see that being a tease-worthy initial set, especially for a girl. But kids can be cruel and find plenty of ways to tease, make fun of, bully, etc. even when initials aren’t taken into account. If the names are names you love, perhaps they flow just as well when reversed? (so initials being MPS instead)… either way, I don’t see it being that big of a deal, except maybe when doing personalized/monogrammed things.
But I totally understand the concern and am in the same boat with the S name struggle. It completely has blocked B names (we don’t want a BS initial baby, although partner said if we found a B name we loved we could go all out and have her initials be BFS 
). It also completely eliminated a name combo I loved—Isolde [name_f]Blair[/name_f] (can’t have an IBS baby, can we?).
Only close friends and family tend to know/use full initials. I might avoid PMS if I had other equally good options, but I think what is more important is avoiding any unfortunate first and last initial acronyms as the middle initial is usually rarely used.
At school everyone will know these initials and you don’t want to make life any harder than it needs to be on the playground! But I don’t see any problems with T.S. or P.S.
(And remember that initials are far far far less important than choosing a name you love!)
I don’t think it should be an issue at all. Especially because middle names aren’t always used when people use nicknames. His other set of initials will however be TS, which many younger people interpret as [name_f]Taylor[/name_f] [name_m]Swift[/name_m].