I'm aware of some of the mores regarding homosexuality in Ancient Rome, like how freeborn males could engage in homosexual relations/sex without a loss in masculinity or status so long as they were the penetrative partner (I'm sure this was likely inconsistent and hiding it would be rather easy).
But what about a Roman Senator in late Republic Rome that was exclusively homosexual? Between let's say the end of the 2nd Punic War and the start of the First Triumvirate. I know that huge public figures like Sulla apparently preferred men, but what about a Patrician statesman that exclusively preferred men? Would this have been bizarre or totally acceptable?
You partly answer your own question with your understanding of Roman views on penetration; a senator who was purely (and willingly) receptive would be viewed as a cinaedus and thus utterly shameful. More interesting to consider, however, is the apparently unusual idea that a vir would be only interested in one sex full stop - whether homosexual or heterosexual.
Craig Williams's superb Roman Homosexuality (p. 187-188) gives some excellent - albeit Imperial, rather than Republican - examples from literature, particularly from Martial (who should perhaps be taken with a pinch of salt as a savagely comic poet), expressing surprise at the idea of someone only being interested in men - or indeed, only women, in the case of Suetonius's discussion of the Emperor Claudius. Even with these slightly gossipy or silly sources, it is striking that there is no corresponding surprise at those who partner both men and women - as long as they are the penetrator.
With regards to the other aspects of your question, by picking the late Republic for your query you've avoided Augustus's lex Iulia which imposed severe penalties on the unmarried and childless; however, Plutarch does mention a Republican tax levied upon bachelors over the age of 60 (although it is unclear whether it would still have been in effect in the late Republic - probably not, given the fact that the lex Iulia were reportedly unpopular in the early Imperial period). More important than marriage was the production of legitimate offspring to continue your family; not having any at all would seem deeply strange in Republican Rome.