Can gay people enter into straight marriages?
With respect, this is a deeply disingenuous argument. It is hardly addressing the point to argue that a lesbian woman, in a long-term relationship with another woman, is perfectly free to leave her partner and marry some random man. It is flippant, irresponsible, and deeply dismissive of the experience of being lesbian or gay.
The argument, moreover, does not stand up to legal scrutiny.
It is well established from case law that a heterosexual marriage where one of the parties is gay or lesbian may be avoided (and thus rendered null and void) on the basis that the party who is gay or lesbian is unable to form and sustain a normal marital relationship with the other party. In UF v JC  ILRM 65 the Supreme Court affirmed that a homosexual orientation may prevent a person from forming and sustaining the necessary relationship with a person of the opposite sex. This may render the marriage voidable. What this means is that the other party may avoid the marriage, in which case the marriage is null and void and of no legal effect, with retrospective effect. Once avoided, it is deemed not to be and never to have been a valid marriage.
Chief Justice Finlay commented that:
"Recognition by psychiatrists of the existence of a homosexual nature and inclination, which is not susceptible to being changed, makes it, in my view, a necessary and permissible development of the law of nullity, having regard to the principles which I have already outlined in this judgment, that it should recognise that in certain circumstances the existence in one party to a marriage of an inherent and unalterable homosexual nature may form a proper legal ground for annulling the marriage at the instance of the other party to the marriage in the case, at least, where that party has no knowledge of the existence of the homosexual nature."Interestingly, it appears also that this is the case in the canon law of the Roman Catholic Church. The homosexuality of one of the spouses may be a ground for annulling a Roman Catholic marriage under the Church's rules relating to the validity of sacramental marriages.
This does not mean that an opposite-sex marriage involving a gay or lesbian person will automatically or always be voidable. A homosexual or bisexual orientation on its own may not be sufficient in every case. Much will depend on the facts. The applicant must be able to show that the relevant party's sexuality made it impossible to sustain a normal and caring marriage relationship. It is arguable that in a good many cases a normal heterosexual marriage relationship may be possible notwithstanding such orientation. In AB v NC  IEHC 127, for instance, a marriage was upheld despite some evidence that the husband was attracted to other men. Notably, the couple had a regular sexual relationship and the husband had not acted on these attractions. It appears, also, that an annulment might not be available if a spouse knew her partner was gay before the marriage. If the spouse knew of the issue and married anyway, they would likely be treated as having lost the right to avoid. If the spouse found out after the marriage and, knowing of the right to avoid, still continued in the marriage, the right to avoid might also be lost.
As a general principle, however, an opposite-sex marriage involving a gay person is at least potentially voidable.
Curiously, the same principle does not, it seems, apply to civil partnership. There is no requirement in law that civil partners be gay or bisexual. Provided neither party is misled or mistaken as to the other party's sexual orientation, the civil partnership, it would appear, is perfectly valid even though one or other party is straight.
There is also case law to the effect that a person who marries someone who is, unbeknownst to them, gay or lesbian may have the marriage declared void. The rationale here is that where a party marries not knowing of a relevant inherent disposition, the marriage may be void for lack of consent. In F v F  1 IR 348 a wife sought a decree of nullity on the basis that her husband was gay and had both before and after their marriage engaged in homosexual relationships. Barron J., in granting the decree, relied primarily on the ground that the respondent lacked the capacity to enter into and sustain a normal marital relationship. He nonetheless had “no doubt” that as a result of the respondent’s failure to reveal the truth, the petitioner’s “consent to the marriage was apparent only and not a true consent". Similarly, in SB v FL  1 IR 521 the High Court declared a marriage void because the wife did not know at the time of the marriage that her husband was transgender. While a marriage cannot be avoided due to concealment of conduct, the concealment of an inherent disposition, such as homosexuality, may still render the marriage void.
Given such case law, the proposition that gay people are free to enter into heterosexual marriage - and thus treated equally in law - falters. The simple fact is that both in state law and under the canon law rules of the Roman Catholic Church, such marriages are vulnerable to being declared invalid.
If the law were changed to permit marriage for same-sex couples, it is interesting to speculate what would happen in this area of law. It would be impossible in such a context to argue that being gay per se would be a barrier to a lawful marriage. It is nonetheless possible that a homosexual orientation would still possibly render a heterosexual marriage voidable, where it prevented the gay spouse from forming and sustaining a normal marriage relationship. By rights, the inverse should also be the case - a marriage between two parties of the same sex involving a heterosexual should equally be voidable, though the point is moot in the absence of case law.