There is considerable debate about who is eligible for vedic rites. The shrauta sUtras, which are the authorities on the topic are quite clear about the matter, barring a few debatable points. kAtyAyana expounds these matters most clearly:
Now we shall explain the eligibility for performing vedic rites.
1.1.2 falyuktAni karmANi
The rites are connected with specific results.
Prima facie everyone is entitled vedic rites as no specification has been made in this regard.
1.1.4 manuShyANAM vA .arambhasAmarthyAt
By this it is meant that only humans who are capable of such actions are eligible.
1.1.5 a~NgahInA .ashrotriya-ShaNDa-shudra-varjaM
Individuals with defective bodies, untrained in the vedas, hermaphrodites and shudras are excluded. [For shudra exceptions see below]
1.1.6 brAhmaNa-rAjanya-vaishyAnAM shruteH
The brahmins, kShatriyas and vaishyas are known to be eligible.
1.1.7 strI chA .avisheShAt
As there is no specification otherwise women are also eligible.
The above is true as it is seen in actual practice. The commentator cites TS 6.1.3 as the authority for this clause: “mekhalayA yajamAnaM dIkShayati yoktreNa patnIM”
1.1.9 rathakArasyA .adhAne
A person of the chariot maker class may set up the sacrificial fires for rituals [agneyadhAna]
1.1.10 niyataM cha
His [rathakAra’s] eligibility also extends to obligatory vedic rites
1.1.11 nA .abhAvAditi vAtsyaH
The [shukla yajurvedic authority] vAtsya is of the opinion that his eligibility does not extend to other vedic rites.
1.1.12 niShAdasthapatir-gAvedhuke .adhikR^itaH
The niShada chieftain is eligible to a vedic ritual with the offerings of gAvedhuka [Coix barbata] (usually to the deity rudra).
1.1.13 vAv.akIrNino gardabhejyA
The optional ass sacrifice may be offered by the fallen student who has had sex.
The niShada sthapati and the fallen student set up their sacrificial fires in an ordinary way (that is non-cermonial)
The other sacrificers use 3 cermonially set up shrauta fires and the aupAsana fire for domestic worship.
Two shrauta sutras proscribe anyone other than a brahmin from being the R^itvik at a sacrifice:
kAtyAyana 1.2.8: brAhmaNA R^itvijo bhakShapratiShedhAditarayoH /
[Of the 3 allowed varNas only] the brahmins can act as officiating priests as the other two are forbidden from eating the sacrificial [remnants]. The commentators cite the authority of the shatapatha brAhmaNa of the shukla yajurveda to support this point.
SB 188.8.131.52: tad vai na abrAhmaNaH pibet (non brahmins do not drink [the remnants of sacrificial beverages])
Apastamba 24.1.21: brAhmaNAnAM ArtvijyaM
The R^itviks duty is that of the brahmins.
However other sutras do not have any prohibitory rules.