It has nothing to do with enmity or friendship between the Grahas. Actually one needs to worship the Grahas in their due order. And, this order is given in the following verse:
Surya (The sun), Soma (the moon), Mahiputra (the son of the earth,
Mars), Somaputra (the son of the moon. Mercury), Brihaspati (Jupiter),
Sukra (Venus), Sanaichara (Saturn), Rahu (the ascending node) and Ketu
(the descending node), these are remembered as Grahas.— (verse 296,
Chapter 12 of Yajnavalkya Smriti.)
So, in the current case, the Mantra for Mars is to be chanted first, then that of Saturn and then, at the last, one should chant the Rahu Mantra.
If it was the case of Mantras of Moon, Mercury and Sun, then it would have been wrong to chant the Mercury Mantra first then the Moon's Mantra and then the Sun's.
Also, as a side note, Mantra Sadhana is not that easy as some people might think it to be. First of all, one needs to be qualified and it is achieved by the Guru Diksha. Secondly, one needs to do Purascharna of a Mantra to make it work for us.
And, it is always wise to do such Sadhanas under the guidance of the Guru. If something goes wrong then your Guru is there to protect you but without the Guru you're completely unprotected.
In the Navagraha Sadhana particularly, if something goes wrong, then the aspirant might have to face the wrath of these planets.
So, it's better to keep these things in mind too as you are chanting the Bija Mantras of the Grahas. If it was the case of chanting of simple Slokas or Stotras then there wouldn't have been anything to worry about.