The term Mleccha has different connotations.
a person like the uncultured people, who is not able to pronounce
words correctly cf. म्लेच्छा मा भूमेत्यध्येयं व्याकरणम् (mlecchā mā
It also indicates a barbarian.
Manu Smriti 7.149 says
जडमूकान्धबधिरांस्तैर्यग्योनान् वयोऽतिगान् ।
स्त्रीम्लेच्छव्याधितव्यङ्गान् मन्त्रकालेऽपसारयेत् ॥ १४९ ॥
jaḍamūkāndhabadhirāṃstairyagyonān vayo'tigān |
strīmleccavyādhitavyaṅgān mantrakāle'pasārayet || 149 ||
At the time of taking counsel, he shall send away the idiot, the dumb
and the deaf, animals, very aged persons, women, foreigners, the sick
and the maimed.
If Pronunciation of Sanskrit in a proper way is taken as the basis for deciding who a Mleccha is, we have to remember that many Hindus also do not know how to pronounce properly, due to English based education.
If birth in Foreign tribes/races is taken as the basis, another question crops up - is it a hurdle to achieve spiritual realisation, which is the Ultimate knowledge even according to Veda?
Then the answer would be No.
Sister Nivedita, Dr. Paul Brunton, David Frawley, etc, with foregin origin achieved what majority of Hindus could not.
Sri Krishna in his Gita, did say about Varnas, a karma based segregation, but not a birth based segregation of humans.
So coming to the aspect of utterance of "OM" by Mleccha, I don't think it is wrong, as every human is entitled to SPIRITUAL KNOWLEDGE, as it is divine.