I don't think there is any problem there. Theravada accepts the bodhisattva path, even if they have a bit different set of 10 paramis. You shouldn't forget either that they were the so called Hinayana schools where the whole bodhisattva concept was developed in the first place.
The early Śrāvakayāna schools had to figure out the origins of their founder the Buddha. However, at least initially it does not seem a significant number of people decided that they too could emulate him and become Buddhas themselves. Moreover, the definition of "Buddha" was not universal. The Sarvāstivāda school, closely related to Theravāda, did not see the Buddha in a transcendental light, while the Mahāsāṃghika did. For the latter school the Bodhisattva path would have seemed far more realistic.
Even in modern Theravāda their definition and vision of a Buddha is quite different from the Mahāyāna. For them the Buddha was an Arhat who restarted the Dharma Wheel in a world where the dharma / dhamma had been lost. They do not accept the transcendental vision of Buddhas and Bodhisattvas as legitimate, let alone canonical. However, the Śrāvakayāna Mahāsāṃghika did at least see the Buddha as something other than a flesh and blood Arhat who restarted the Dharma Wheel in a world where it had been lost.
Basically, there is a irreconcilable difference in the goals of Theravāda and all extant Mahāyāna schools. It is not a problem if we accept that difference, but not everyone does. The Mahāyāna generally accepts the Arhat path as legitimate, but Theravāda will generally reject the Mahāyāna vision of Buddhahood.
In reality the issue of sectarianism is not the fault of the Mahāyāna.
On the other hand, I've read somewhere the idea that in those Mahayana communities where they teach "buddhahood in this life" it is in fact reaching arhatship it's just that they had to change the terminology.
If you actually believe in rebirth, then the difference between a Bodhisattva and Arhat is quite simple: the former voluntarily takes rebirth for the benefit of others while the other seeks cessation of all existence. The Arhat can have compassion and teach the dharma while he or she is alive, but at death they are not of much direct benefit to sentient beings.
Anyway, I believe this is a marginal matter compared to actually looking at the very teachings and practices different schools use. It is there to find the singular nature of the path consisting of morality (harmlessness and kindness), meditation (samatha and vipasyana) and wisdom (selflessness and dependent origination).
It is not a marginal matter.
If you wish to aid in the liberation of all sentient beings, even if it means you have to take rebirth for immeasurable kalpas, you adopt the Bodhisattva path. If you want freedom from your suffering and cessation of rebirth, you take the Arhat path.
If you don't believe in rebirth, then the goals of Arhatship and Bodhisattvahood are entirely void of meaning, in which case Buddhism is of little use to you.