I remember to have read (in the Shulchan Aruch I believe) that after doing the Netilat Yadayim one can't touch one's hair, because that would make you impure again. But when I put on and accommodate my Tefilin, I inevitably touch my hair. This seems paradoxical, but maybe I got some facts wrong. Can one touch his hair between Netilah and Tefillin?
The source of all poskim at regard of this subject is in Rashba.Shut Harashba (I, 755). See bellow a copy of this text, with explanations and notes are given in brackets.
He were asked again. Regarding our following custom: We must be careful not to touch soiled places (paraphrasing of Gemara Brachot 24b) at prayer time and at mealtime. What areas are called soiled?According to all poskim the subject matter of this responsa is "dirt particles" (we may imagine to object against the Eshel Avraham cited bellow).
He responded: It is likely that not only the soiled areas strictly speaking; but also the calf, the thigh, covered (with clothing) in humans, because there is sweat ("on them" following the printed edition) ["little balls of sweat" following the quoted snippet in Bet Yossef]. Scratching the head also (falls into this category)
But open areas of the head (may be the skull area is called head as in nazir) and the face, open areas of the upper arms, are not spoiled areas because lake of feces or sweat. Such is the custom.
Hands become defiled after contact with covered skinI.E. skin that is covered, or by clothes or by hairs S.A. O.C. 4. 21. It is because of sweat. Hair itself is not a problem. "Facial hair covered skin" is not a problem because the sweat of this skin is not "harmful", (the mnemonic verse is "In the sweat of thy face shalt thou eat bread", Genesis 3, 19).
The problem is that a skin usually covered is all the time dirty or sweaty.
If the covered skin is clean (bodily cleanness)See Eshel Avraham Botshatsh (4, 21). He wrote that Chachomim decreed a "lo plug" and touching clean covered skin (his understanding of Shut Harashba is that something was ruled). For example after a good shower, we need to wash hands.
Apparently touching hairs, doe's not rise problem 'per se'; but rub or scratch is a real problem.See Shulchan Aruch O.C. 4, 21 "לחכך בראש". After scratching his head one must to wash their hands. (In Piskey Teshuva, in name of Rav Wozner, Shut Shevet Halevi, it is allowed to scratching head in area not covered by hat or Kippa as says Dude)
So, touching one's hair (if they are dried) while putting on tefilin is allowed.
But if sweat is dripping from hairsone must wash its hands. Eshel Avraham B. has infered from S.A. siman 4 that Tefilin of head are on open areas of the head. But he is reluctant to this idea because hair zones (excepting facial hairs skin) are always considered as covered skin. He do not resolve the question. So if the scalp or Tefilin of head hare sweaty, one should consider to wash hand after contact with them.
- Touching the skin of the upper arm should hypothetically be more problematic See in the Machatsit Hashekel (4, sk 23), see Mishna brura sk 53 and Beur halacha (In a country, people do not cover calf, so calf is an open area. May be that E.A. agrees and lo plug is only in a same country. The Beur Halacha is hard to understanding). but the he Eshel Avraham B. says that Tefilin on upper arm covered in sweat may be touched with hands without any problem. He thinks that Tefilin are putting on open skin areas. So we can touch this sweat.
If someone is baldI am not in position to answer if this changes something to the status of scalp skin.
specifically the shulchan aruch refers to hair which is under your yarmulke b/c it would normally be covered. One of the reasons we wash our hands first thing in the morning is our hands could have been moving around while we were sleeping and touched a part of our body normally covered.
See my answer here which specifically references the shulchan aruch harav Why are we impure when we wake up? that discuses the reasons for being tame first thing in the morning and needing to wash one's hands.
The Shulchan Aruch also discuses the idea of touching parts of the body normally covered in siman daled in reference to washing in the morning.