Does there exist a Pali Canon sutta that claims that a Bodhisattva can only be a male Brahmin or Kshatriya? If yes, is it possibly apocryphal?

Virtue and learning I was fain to test;
Henceforth I doubt not virtue is the best.
Virtue excels vain gifts of form and birth,
Apart from virtue learning has no worth.
A prince or peasant, if to sin enslaved,
In neither world front misery is saved.
Men of high caste with those of base degree,
If virtuous here, in heaven will equal be.
Not birth, nor lore, nor friendship aught avails,
Pure virtue only future bliss entails.

— Stories of the Buddha’s Former Births Book 5 Pañcanipāta 362. Silavimamsa Jātaka

At the end of his life, the Buddha unwittingly got involved in political intrigue when Varsakara, a minister of the Magadha kingdom, asked him for the secret of the strength of the Republican states. Among the seven unfailing factors of the strength of a society, he included “sticking to ancient laws and traditions” and “maintaining sacred sites and honoring ancient rituals”.

— Digha Nikaya 2:73

The following sutta quotes from Gihi Sutta and Sundarika Sutta show that a person of any caste, social class or background can become an Arahat. The Therigatha has numerous examples of women who became Arahats.

From the Gihi Sutta (AN 5.179):

In the same way,
wherever one is born
among human beings —
noble warriors, brahmans,
merchants, workers,
outcastes, or scavengers —
if one is tame,
with good practices,
righteous,
consummate in virtue,
a speaker of truth,
with conscience at heart,
one who's abandoned birth & death,
completed the holy life
put down the burden,
done the task
fermentation-free,
gone beyond all dhammas,
through lack of clinging
unbound:
offerings to this spotless field
bear an abundance of fruit.

From the Sundarika Sutta (SN 7.9):

Then Sundarika the brahmin went up to the Buddha, and said to him: “Sir, in what caste were you born?”

“Don’t ask about birth, ask about conduct.
For any wood can surely generate fire.
A steadfast sage, even though from a low class family,
is a thoroughbred checked by conscience.

However, is it true that only a brahmana or kshatriya can become a Buddha?

I think it's the other way round. The Mahāpadāna Sutta quoted by that paper simply implies that the bodhisattvas (the beings intent on awakening) tend to have a karmic background that usually results in favourable birth destinations, rather than stating that the bodhisattvas can NEVER be of lower castes.

For e.g. professional basketball players tend to be tall persons, but it does not mean that ONLY tall persons can become professional basketball players.

We can relate from the Tamonata Sutta quote below that the bodhisattvas tend to be persons in light who are headed for light, by virtue of their good conduct and mindset:

"And how is one the type of person in darkness who is headed for light? There is the case where a person is born into a lower class family — the family of a scavenger, a hunter, a basket-weaver, a wheelwright, or a sweeper — a family that is poor, with little food or drink, living in hardship, where food & clothing are hard to come by. And he is ugly, misshapen, stunted, & sickly: half-blind or deformed or lame or crippled. He doesn't receive any [gifts of] food, drink, clothing, or vehicles; garlands, perfumes, or ointments; bedding, shelter, or lamps. He engages in good bodily conduct, good verbal conduct, & good mental conduct. Having engaged in good bodily conduct, good verbal conduct, & good mental conduct, he — on the break-up of the body, after death — reappears in the good destination, the heavenly world. This is the type of person in darkness who is headed for light. .....

"And how is one the type of person in light who is headed for light? There is the case where a person is born into an upper class family — a noble warrior family, a priestly family, a prosperous householder family — a family that is rich, with much wealth, with many possessions, with a great deal of money, a great many accoutrements of wealth, a great many commodities. And he is well-built, handsome, extremely inspiring, endowed with a lotus-like complexion. He receives [gifts of] food, drink, clothing, & vehicles; garlands, perfumes, & ointments; bedding, shelter, & lamps. He engages in good bodily conduct, good verbal conduct, & good mental conduct. Having engaged in good bodily conduct, good verbal conduct, & good mental conduct, he — on the break-up of the body, after death — reappears in the good destination, the heavenly world. This is the type of person in light who is headed for light.

Additional quote from "Buddhism in a Nutshell" by Ven. Narada Mahathera, to show that people from not-so-favourable backgrounds joined the monastic order, and became arahats or otherwise important members:

It was the Buddha who first attempted to abolish slavery and vehemently protested against the degrading caste system which was firmly rooted in the soil of India. In the Word of the Buddha it is not by mere birth one becomes an outcast or a noble, but by one's actions. Caste or color does not preclude one from becoming a Buddhist or from entering the Order. Fishermen, scavengers, courtesans, together with warriors and Brahmans, were freely admitted to the Order and enjoyed equal privileges and were also given positions of rank. Upali, the barber, for instance, was made in preference to all other the chief in matters pertaining to Vinaya discipline. The timid Sunita, the scavenger, who attained Arhatship was admitted by the Buddha Himself into the Order. Angulimala, the robber and criminal, was converted to a compassionate saint. The fierce Alavaka sought refuge in the Buddha and became a saint. The courtesan Ambapali entered the Order and attained Arhatship. Such instances could easily be multiplied from the Tipitaka to show that the portals of Buddhism were wide open to all, irrespective of caste, color or rank.