Short answer; probably.
Grants are likely to be taxable unless they are specifically excluded from tax.
If the grant relates to your continuing business activities, then it is likely to be included in assessable income for income tax purposes. The position can be different in cases where the payment is made so that the entity can commence a new business or cease carrying on a business.
Government grants are not generally subject to GST unless the grant is for a supply of something. The ATO has indicated that the cashflow boost and JobKeeper payments are not subject to GST, this seems to be on the basis that they are not consideration for a supply.
Normally, we look at whether the entity has to do something to obtain the payment / grant. This could include entering into an agreement to do something or refrain from doing something. If not, there won't generally be any GST because no supply is or has been made.
JobKeeper turnover calculations
If GST does not apply to the grant, then it should not be included in the decline in turnover test for the initial phase of JobKeeper or the GST turnover figures that are reported to the ATO on a monthly basis by entities that are participating in JobKeeper.
The exception is the university sector where core Commonwealth Government financial assistance provided is included in the JobKeeper turnover tests.